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EXHIBIT 10.4


                                 FIRST AMENDMENT
                                       TO
                 NEON COMMUNICATIONS, INC. STOCK INCENTIVE PLAN

         WHEREAS, NEON Communications, Inc. (the "COMPANY") heretofore adopted
the NEON Communications, Inc. Stock Incentive Plan (the "PLAN") for the purposes
set forth therein;

         WHEREAS, pursuant to the terms of the Agreement and Plan of Merger,
dated as of July 19, 2004, and the First Amendment to the Agreement and Plan of
Merger, dated October 8, 2004 (together the "MERGER AGREEMENT"), by and between
the Company and Globix Corporation ("GLOBIX"), the Company will merge with and
into a new wholly-owned subsidiary of Globix, and the Company will survive the
merger;

         WHEREAS, pursuant to the terms of the Merger Agreement, all options
outstanding at the effective time of the merger (the "EFFECTIVE TIME") shall be
modified for options to purchase Globix common stock; and

         WHEREAS, the Company has determined that the Plan should be amended to
provide for the issuance of Globix common stock upon exercise of options under
the Plan on or after the Effective Time;

         NOW, THEREFORE, the Plan is hereby amended as follows:

1. Section 1 of the Plan shall be amended to read as follows:

                  "1. PURPOSE. The purpose of the NEON Communications, Inc.
         Stock Incentive Plan (as amended from time to time, the "Plan") is to
         promote the interests of NEON Communications, Inc., a Delaware
         corporation (the "Company"), and any Parent or Subsidiary thereof and
         the interests of the Company's stockholders by providing an opportunity
         to selected employees, directors and officers of, and consultants to,
         the Company or any Parent or Subsidiary thereof as of the date of the
         adoption of the Plan or at any time thereafter to purchase common stock
         of Globix Corporation ("Globix"). By encouraging such stock ownership,
         the Company seeks to attract, retain and motivate such employees,
         directors and officers and other persons and to encourage such
         employees, directors and officers and other persons to devote their
         best efforts to the business and financial success of the Company.

2. All references to "Common Stock of the Company" or the "Company's Common
Stock" shall be deemed to refer to the common stock of Globix Corporation and
section 2.5 of the Plan shall be amended to read as follows:

         "2.5 "COMMON STOCK" shall mean the common stock $.01 par value of
Globix Corporation."

3. Section 16 shall be added to the Plan to read as follows:

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         "Section 16.  Exchange of NEON Options.

         Pursuant to the terms of the Agreement and Plan of Merger, dated as of
July 19, 2004, and the First Amendment to the Agreement and Plan of Merger,
dated October 8, 2004 (together the "MERGER AGREEMENT"), by and between the
Company and Globix Corporation ("GLOBIX") as of the "Effective Time" (as defined
in the Merger Agreement) all Options issued under the Plan that have not been
exercised as of the Effective Time shall be modified for options to purchase
shares of Globix stock pursuant to the adjustment provisions of Section 9 and
the Merger Agreement. After the Effective Time, no additional Options shall be
issued under the Plan."


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