UNITED STATES
                      SECURITIES AND EXCHANGE COMMISSION
                            Washington, D.C.  20549

                                   ----------

                               AMENDMENT NO. 1 TO
                                 SCHEDULE 13G

                   Under the Securities Exchange Act of 1934

                               GLOBIX CORPORATION
--------------------------------------------------------------------------------
                                (Name of Issuer)


                          Common Stock, $.01 par value
--------------------------------------------------------------------------------
                         (Title of Class of Securities)

                                   37957F200
                      ------------------------------------
                                 (CUSIP Number)

                                 March 7, 2005
--------------------------------------------------------------------------------
            (Date of Event Which Requires Filing of this Statement)


Check the appropriate box to designate the rule pursuant to which this Schedule
is filed:

          [_]  Rule 13d-1(b)

          [X]  Rule 13d-1(c)

          [_]  Rule 13d-1(d)




CUSIP No. 37957F200
--------------------------------------------------------------------------------
1.   Name of Reporting Persons
     I.R.S. Identification Nos. of above persons (entities only)

     LC Capital Master Fund, Ltd.
--------------------------------------------------------------------------------
2.   Check the Appropriate Box If a Member of a Group (See Instructions)
     (a)  [_]
     (b)  [_]
--------------------------------------------------------------------------------
3.   SEC Use Only

--------------------------------------------------------------------------------
4.   Citizenship or Place of Organization

     Cayman Islands
--------------------------------------------------------------------------------
               5.   Sole Voting Power
  NUMBER OF         0 shares
   SHARES      -----------------------------------------------------------------
BENEFICIALLY   6.   Shared Voting Power
  OWNED BY          5,363,639 shares
    EACH       -----------------------------------------------------------------
  REPORTING    7.   Sole Dispositive Power
   PERSON           0 shares
    WITH:      -----------------------------------------------------------------
               8.   Shared Dispositive Power
                    5,363,639 shares
--------------------------------------------------------------------------------
9.   Aggregate Amount Beneficially Owned by Each Reporting Person
     363,639 shares
--------------------------------------------------------------------------------
10.  Check Box If the Aggregate Amount in Row (9) Excludes Certain Shares
     CERTAIN SHARES*                                                       [_]
--------------------------------------------------------------------------------
11.  Percent of Class Represented by Amount in Row (9)
     10.9 %
--------------------------------------------------------------------------------
12.  Type of Reporting Person (See Instructions)
     CO
--------------------------------------------------------------------------------

*See Instructions.


CUSIP No. 37957F200
--------------------------------------------------------------------------------
1.   Name of Reporting Persons
     I.R.S. Identification Nos. of above persons (entities only)

     LC Capital Partners, L.P.
--------------------------------------------------------------------------------
2.   Check the Appropriate Box If a Member of a Group (See Instructions)
     (a)  [_]
     (b)  [_]
--------------------------------------------------------------------------------
3.   SEC Use Only

--------------------------------------------------------------------------------
4.   Citizenship or Place of Organization

     Delaware
--------------------------------------------------------------------------------
               5.   Sole Voting Power
  NUMBER OF         0 shares
   SHARES      -----------------------------------------------------------------
BENEFICIALLY   6.   Shared Voting Power
  OWNED BY          5,363,639 shares
    EACH       -----------------------------------------------------------------
  REPORTING    7.   Sole Dispositive Power
   PERSON           0 shares
    WITH:      -----------------------------------------------------------------
               8.   Shared Dispositive Power
                    5,363,639 shares
--------------------------------------------------------------------------------
9.   Aggregate Amount Beneficially Owned by Each Reporting Person
     373,141 shares
--------------------------------------------------------------------------------
10.  Check Box If the Aggregate Amount in Row (9) Excludes Certain Shares
     CERTAIN SHARES*                                                      [_]
--------------------------------------------------------------------------------
11.  Percent of Class Represented by Amount in Row (9)
     11.0%
--------------------------------------------------------------------------------
12.  Type of Reporting Person (See Instructions)
     PN, HC
--------------------------------------------------------------------------------

*See Instructions.



CUSIP No. 37957F200
--------------------------------------------------------------------------------
1.   Name of Reporting Persons
     I.R.S. Identification Nos. of above persons (entities only)

     LC Capital Advisors LLC
--------------------------------------------------------------------------------
2.   Check the Appropriate Box If a Member of a Group (See Instructions)
     (a)  [_]
     (b)  [_]
--------------------------------------------------------------------------------
3.   SEC Use Only

--------------------------------------------------------------------------------
4.   Citizenship or Place of Organization

     Delaware
--------------------------------------------------------------------------------
               5.   Sole Voting Power
  NUMBER OF         0 shares
   SHARES      -----------------------------------------------------------------
BENEFICIALLY   6.   Shared Voting Power
  OWNED BY          5,363,639 shares
    EACH       -----------------------------------------------------------------
  REPORTING    7.   Sole Dispositive Power
   PERSON           0 shares
    WITH:      -----------------------------------------------------------------
               8.   Shared Dispositive Power
                    5,363,639 shares
--------------------------------------------------------------------------------
9.   Aggregate Amount Beneficially Owned by Each Reporting Person
     5,363,639 shares
--------------------------------------------------------------------------------
10.  Check Box If the Aggregate Amount in Row (9) Excludes Certain Shares
     CERTAIN SHARES*                                                      [_]
--------------------------------------------------------------------------------
11.  Percent of Class Represented by Amount in Row (9)
     10.9%
--------------------------------------------------------------------------------
12.  Type of Reporting Person (See Instructions)
     OO, HC
--------------------------------------------------------------------------------

*See Instructions.



CUSIP No. 37957F200
--------------------------------------------------------------------------------
1.   Name of Reporting Persons
     I.R.S. Identification Nos. of above persons (entities only)

     Lampe, Conway & Co. LLC
--------------------------------------------------------------------------------
2.   Check the Appropriate Box If a Member of a Group (See Instructions)
     (a)  [_]
     (b)  [_]
--------------------------------------------------------------------------------
3.   SEC Use Only

--------------------------------------------------------------------------------
4.   Citizenship or Place of Organization

     Delaware
--------------------------------------------------------------------------------
               5.   Sole Voting Power
  NUMBER OF         0 shares
   SHARES      -----------------------------------------------------------------
BENEFICIALLY   6.   Shared Voting Power
  OWNED BY          5,363,639 shares
    EACH       -----------------------------------------------------------------
  REPORTING    7.   Sole Dispositive Power
   PERSON           0 shares
    WITH:      -----------------------------------------------------------------
               8.   Shared Dispositive Power
                    5,363,639 shares
--------------------------------------------------------------------------------
9.   Aggregate Amount Beneficially Owned by Each Reporting Person
     5,363,639 shares
--------------------------------------------------------------------------------
10.  Check Box If the Aggregate Amount in Row (9) Excludes Certain Shares
     CERTAIN SHARES*                                                      [_]
--------------------------------------------------------------------------------
11.  Percent of Class Represented by Amount in Row (9)
     10.9%
--------------------------------------------------------------------------------
12.  Type of Reporting Person (See Instructions)
     OO, IV
--------------------------------------------------------------------------------

*See Instructions.



CUSIP No. 37957F200
--------------------------------------------------------------------------------
1.   Name of Reporting Persons
     I.R.S. Identification Nos. of above persons (entities only)

     LC Capital International LLC
--------------------------------------------------------------------------------
2.   Check the Appropriate Box If a Member of a Group (See Instructions)
     (a)  [_]
     (b)  [_]
--------------------------------------------------------------------------------
3.   SEC Use Only

--------------------------------------------------------------------------------
4.   Citizenship or Place of Organization

     Delaware
--------------------------------------------------------------------------------
               5.   Sole Voting Power
  NUMBER OF         0 shares
   SHARES      -----------------------------------------------------------------
BENEFICIALLY   6.   Shared Voting Power
  OWNED BY          5,363,639 shares
    EACH       -----------------------------------------------------------------
  REPORTING    7.   Sole Dispositive Power
   PERSON           0 shares
    WITH:      -----------------------------------------------------------------
               8.   Shared Dispositive Power
                    5,363,639 shares
--------------------------------------------------------------------------------
9.   Aggregate Amount Beneficially Owned by Each Reporting Person
     5,363,639 shares
--------------------------------------------------------------------------------
10.  Check Box If the Aggregate Amount in Row (9) Excludes Certain Shares
     CERTAIN SHARES*                                                      [_]
--------------------------------------------------------------------------------
11.  Percent of Class Represented by Amount in Row (9)
     10.9%
--------------------------------------------------------------------------------
12.  Type of Reporting Person (See Instructions)
     OO, IA
--------------------------------------------------------------------------------

*See Instructions.



CUSIP No. 37957F200
--------------------------------------------------------------------------------
1.   Name of Reporting Persons
     I.R.S. Identification Nos. of above persons (entities only)

     Steven G. Lampe
--------------------------------------------------------------------------------
2.   Check the Appropriate Box If a Member of a Group (See Instructions)
     (a)  [_]
     (b)  [_]
--------------------------------------------------------------------------------
3.   SEC Use Only

--------------------------------------------------------------------------------
4.   Citizenship or Place of Organization

     United States
--------------------------------------------------------------------------------
               5.   Sole Voting Power
  NUMBER OF         0 shares
   SHARES      -----------------------------------------------------------------
BENEFICIALLY   6.   Shared Voting Power
  OWNED BY          5,373,141 shares
    EACH       -----------------------------------------------------------------
  REPORTING    7.   Sole Dispositive Power
   PERSON           0 shares
    WITH:      -----------------------------------------------------------------
               8.   Shared Dispositive Power
                    5,373,141 shares
--------------------------------------------------------------------------------
9.   Aggregate Amount Beneficially Owned by Each Reporting Person
     5,363,639 shares
--------------------------------------------------------------------------------
10.  Check Box If the Aggregate Amount in Row (9) Excludes Certain Shares
     CERTAIN SHARES*                                                      [_]
--------------------------------------------------------------------------------
11.  Percent of Class Represented by Amount in Row (9)
     10.9%
--------------------------------------------------------------------------------
12.  Type of Reporting Person (See Instructions)
     IN
--------------------------------------------------------------------------------

*See Instructions.




CUSIP No. 37957F200
--------------------------------------------------------------------------------
1.   Name of Reporting Persons
     I.R.S. Identification Nos. of above persons (entities only)

     Richard F. Conway
--------------------------------------------------------------------------------
2.   Check the Appropriate Box If a Member of a Group (See Instructions)
     (a)  [_]
     (b)  [_]
--------------------------------------------------------------------------------
3.   SEC Use Only

--------------------------------------------------------------------------------
4.   Citizenship or Place of Organization

     United States
--------------------------------------------------------------------------------
               5.   Sole Voting Power
  NUMBER OF         0 shares
   SHARES      -----------------------------------------------------------------
BENEFICIALLY   6.   Shared Voting Power
  OWNED BY          5,363,639 shares
    EACH       -----------------------------------------------------------------
  REPORTING    7.   Sole Dispositive Power
   PERSON           0 shares
    WITH:      -----------------------------------------------------------------
               8.   Shared Dispositive Power
                    5,363,639 shares
--------------------------------------------------------------------------------
9.   Aggregate Amount Beneficially Owned by Each Reporting Person
     5,363,639 shares
--------------------------------------------------------------------------------
10.  Check Box If the Aggregate Amount in Row (9) Excludes Certain Shares
     CERTAIN SHARES*                                                      [_]
--------------------------------------------------------------------------------
11.  Percent of Class Represented by Amount in Row (9)
     10.9%
--------------------------------------------------------------------------------
12.  Type of Reporting Person (See Instructions)
     IN
--------------------------------------------------------------------------------

*See Instructions.




Item 1(a).        Name of Issuer:
                  

                  GLOBIX CORPORATION


Item 1(b).        Address of Issuer's Principal Executive Offices:

                  139 Centre Street
                  New York, NY 10013

Item 2(a).        Name of Person Filing:

                  Pursuant to Rule 13d-1(k)(1) under the Securities Exchange Act
of 1934, as amended, this Schedule 13G is filed on behalf of each of the
reporting persons indicated in Item 1 of each of the cover pages of this
Schedule 13G. The information required by this paragraph is set forth in Item 1
of each of the cover pages of this Schedule 13G and is incorporated herein by
reference.

Item 2(b).        Address of Principal Business Office or, if None, Residence:

                  The information required by this paragraph is set forth on
Annex A attached hereto and is incorporated herein by reference.

Item 2(c).        Citizenship:

                  The information required by this paragraph is set forth in
Item 4 of each of the cover pages of this Schedule 13G and is incorporated
herein by reference.


Item 2(d).        Title of Class of Securities:

                  common stock, $.01 par value ("Common Stock")


Item 2(e).        CUSIP Number:

                  37957F200


Item 3.           Not applicable.


Item 4.           Ownership.

                  (a) Amount Beneficially Owned:

                  The information required by this paragraph is set forth in
Item 9 of each of the cover pages of this Schedule 13G and is incorporated
herein by reference.

                  LC Capital Master Fund, Ltd. (the "Master Fund") directly
holds 4,901,177 shares of the Issuer's Common Stock, par value $0.01 per share
(the "Common Stock") and 462,462 shares of the Issuer's preferred stock (the
"Preferred Stock" and together with the Common Stock the "Shares"), which is
convertible into Common Stock on a share-for-share basis. The Shares were
acquired in separate transactions as follows: 770,646 shares of Common Stock
were acquired on October 16, 2002; 449,171 shares of Common Stock were acquired
on September 22, 2003; and 3,226,815 shares of Common Stock and 462,462 shares



of Preferred Stock were acquired on the conversion of common stock and preferred
stock of NEON Communications, Inc. ("NEON") into shares of Common Stock and
Preferred Stock in connection with the merger of NEON with a subsidiary of the
Issuer on March 7, 2005 (the "Merger"). The Shares listed above also include
454,545 shares of Common Stock acquired upon a debt-for-equity exchange with the
Issuer that took place concurrently with the Merger. In the Merger, Steven C.
Lampe also acquired an option to purchase 9,502 shares of Common Stock upon the
conversion of options to purchase NEON common stock issuable under the NEON 2003
Directors' Stock Option Plan.
.
                  LC Capital Partners, LP ("Partners") may be deemed to control
the Master Fund by virtue of Partners' ownership of approximately 54.31% of the
outstanding shares of the Master Fund. Accordingly, Partners may be deemed to
have a beneficial interest in the Shares. In addition, since LC Capital Advisors
LLC ("Advisors") is the sole general partner of Partners, Advisors may also be
deemed to have a beneficial interest in the Shares. Each of Partners and
Advisors disclaims beneficial ownership of the Shares except to the extent of
their respective beneficial interests, if any, therein.

                  Lampe, Conway & Co. LLC ("LC&C") acts as investment manager to
Partners and the Master Fund pursuant to certain investment management
agreements. LC Capital International LLC ("International") acts as investment
advisor to the Master Fund pursuant to an investment advisory agreement. Since
LC&C and International share voting and dispositive power over the Shares by
virtue of the aforementioned agreements (the "Agreements"), LC&C and
International may each be deemed to have a beneficial interest in the Shares.
Each of LC&C and International disclaims beneficial ownership of the Shares
except to the extent of their respective beneficial interests, if any, therein.

                  Steven G. Lampe ("Lampe") and Richard F. Conway ("Conway") act
as the sole managing members of each of Advisors, LC&C and International and
each of Lampe and Conway may be deemed to control each such entity. Accordingly,
each of Lampe and Conway may be deemed to have a beneficial interest in the
Shares by virtue of Advisors' indirect deemed control of the Master Fund and
LC&C's and International's respective power to vote and/or dispose of the Shares
pursuant to the Agreements. Each of Lampe and Conway disclaims beneficial
ownership of the Shares except to the extent of their respective beneficial
interests, if any, therein.

                  (b) Percent of Class:

                  The information required by this paragraph is set forth in
Item 11 of each of the cover pages of this Schedule 13G and is incorporated
herein by reference. The information in Item 4(a) above is incorporated herein
by reference.

                  (c) Number of shares as to which such person has:

                           (i) Sole power to vote or to direct the vote:

                  The information required by this subparagraph is set forth in
Item 5 of each of the cover pages of this Schedule 13G and is incorporated
herein by reference. In addition, the information in Item 4(a) above is
incorporated herein by reference.

                           (ii) Shared power to vote or to direct the vote:

                  The information required by this subparagraph is set forth in
Item 6 of each of the cover pages of this Schedule 13G and is incorporated
herein by reference. In addition, the information in Item 4(a) above is
incorporated herein by reference.



                           (iii) Sole power to dispose or to direct the
disposition of:

                  The information required by this subparagraph is set forth in
Item 7 of each of the cover pages of this Schedule 13G and is incorporated
herein by reference. In addition, the information in Item 4(a) above is
incorporated herein by reference.

                           (iv) Shared power to dispose or to direct the
disposition of:

                  The information required by this subparagraph is set forth in
Item 8 of each of the cover pages of this Schedule 13G and is incorporated
herein by reference. In addition, the information in Item 4(a) above is
incorporated herein by reference.

Item 5.           Ownership of Five Percent or Less of a Class.

                  If this statement is being filed to report the fact that as of
                  the date hereof the reporting person has ceased to be the
                  beneficial owner of more than five percent of the class of
                  securities, check the following [ ].

Item 6.           Ownership of More Than Five Percent on Behalf of Another 
                  Person.

                  Not Applicable

Item 7.           Identification and Classification of the Subsidiary Which
                  Acquired the Security Being Reported on by the Parent Holding
                  Company or Control Person.

                  The Master Fund directly acquired all of the Shares being
reported on by Partners and Advisors. Partners directly holds approximately
54.31% of the outstanding shares of the Master Fund and may be deemed to control
the Master Fund. Advisors is the sole general partner of Partners and may also
be deemed to control the Master Fund.


Item 8.           Identification and Classification of Members of the Group.

                  Not Applicable


Item 9.           Notice of Dissolution of Group.

                  Not applicable

Item 10.          Certification.


                  By signing below, each of the undersigned certifies that, to
the best of his or its knowledge and belief, the securities referred to above
were not acquired and are not held for the purpose of or with the effect of
changing or influencing the control of the issuer of the securities and were not
acquired and are not held in connection with or as a participant in any
transaction having that purpose or effect.






                                    SIGNATURE

                  After reasonable inquiry and to the best of my knowledge and
belief, the undersigned certifies that the information set forth in this
statement is true, complete and correct


Date: April 15, 2005                     LC Capital Master Fund, Ltd.

                                          By: /s/ LC Capital Master Fund, Ltd.
                                              ----------------------------------
                                              Name: 
                                              Title: 


Date: April 15, 2005                      LC Capital Partners, LP

                                          By: LC Capital Advisors LLC,
                                              its General Partner

                                          By: /s/ LC Capital Partners, LP
                                              ----------------------------------
                                              Name: 
                                              Title: 


Date: April 15, 2005                      LC Capital Advisors LLC

                                          By:  /s/ LC Capital Advisors LLC
                                              ----------------------------------
                                              Name: 
                                              Title: 


Date: April 15, 2005                      Lampe, Conway & Co. LLC

                                          By: /s/ Lampe, Conway & Co. LLC
                                              ----------------------------------
                                              Name: 
                                              Title: 


Date: April 15, 2005                      LC Capital International LLC

                                          By: /s/ LC Capital International LLC
                                              ----------------------------------
                                              Name: 
                                              Title: 


Date: April 15, 2005                      /s/ Steven G. Lampe
                                          --------------------------------------
                                          Steven G. Lampe


Date: April 15, 2005                      /s/ Richard F. Conway
                                          --------------------------------------
                                          Richard F. Conway





                                                                         ANNEX A
                                                                         -------

           Address of Principal Business Office or, if none, Residence
           -----------------------------------------------------------

LC Capital Master Fund, Ltd.
c/o Trident Fund Services (B.V.I.) Limited
P.O. Box 146
Waterfront Drive
Wickhams Cay
Road Town, Tortola
British Virgin Islands

LC Capital Partners, LP
680 Fifth Avenue, Suite 1202
New York, NY  10019

LC Capital Advisors LLC
680 Fifth Avenue, Suite 1202
New York, NY  10019

Lampe, Conway & Co. LLC
680 Fifth Avenue, Suite 1202
New York, NY  10019

LC Capital International LLC
680 Fifth Avenue, Suite 1202
New York, NY  10019

Steven G. Lampe
680 Fifth Avenue, Suite 1202
New York, NY  10019

Richard F. Conway
680 Fifth Avenue, Suite 1202
New York, NY  10019