<PAGE>   1
                                                                   EXHIBIT 10.4

                            ASSIGNMENT OF SECURITIES

         This Assignment of Securities ("Assignment") is entered into as of
June 26, 2000, by and between HMTF Bridge Globix, LLC, a Delaware limited
liability company (the "Assignor"), and HM4 Globix Qualified Fund, LLC, a
Delaware limited liability company, HM4 Globix Private Fund, LLC, a Delaware
limited liability company, HM PG-IV Globix, LLC, a Delaware limited liability
company, HM 4-SBS Globix Coinvestors, LLC, a Delaware limited liability
company, and HM 4-EQ Globix Coinvestors, LLC, a Delaware limited liability
company (collectively, the "Assignees").

                                    RECITALS

         A. HMTF-IV Acquisition Corp. entered into that certain Stock Purchase
Agreement, dated as of November 5, 1999 (the "Purchase Agreement"), by and
between HMTF-IV Acquisition Corp. and Globix Corporation (the "Company").
Capitalized terms not otherwise defined herein shall have the meanings ascribed
to such terms in the Purchase Agreement.

         B. On the terms of the Purchase Agreement, HMTF-IV Acquisition Corp.
agreed to purchase, and the Company agreed to sell, 80,000 shares of the
Company's Series A 7.5% Convertible Preferred Stock (the "Purchased
Securities"). Pursuant to that certain Assignment of Rights Under Stock
Purchase Agreement, dated November 9, 1999 ("First Assignment of Rights"), by
and between HMTF-IV Acquisition Corp., as assignor, and the Assignees, as
Assignees, HMTF-IV Acquisition Corp. assigned all of its rights, titles, and
interests in, to, and under the Purchase Agreement with respect to the
Purchased Securities, to the Assignees.

         C. Pursuant to that certain Assignment of Rights Under Stock Purchase
Agreement, dated November 16, 1999 ("Second Assignment of Rights"), by and
between Assignees, as assignor, and Assignor, as assignee, the Assignees
assigned to Assignor all of Assignees' rights, titles and interests in, to and
under the Purchase Agreement with respect to 20,000 shares of the Purchased
Securities in the proportions reflected on Exhibit A attached hereto.

         D. Assignor now desires to sell and assign to Assignees all of
Assignor's rights, titles, and interests in, to, and under the Purchase
Agreement with respect to its 20,000 shares of the Purchased Securities in the
proportions reflected on Exhibit A attached hereto.

                                   AGREEMENTS

         NOW, THEREFORE, in consideration of the covenants of Assignees
hereunder and for other good and valuable consideration, the receipt and
sufficiency of which are hereby acknowledged, the parties hereto, intending to
be legally bound, hereby agree as follows:

         1. ASSIGNMENT. Assignor hereby sells, assigns, transfers, and conveys
to each Assignee and its respective successors and assigns the percentage of
Assignor's rights, titles, interests, and

<PAGE>   2

obligations in, to, and under the Purchase Agreement as set forth opposite such
Assignee's name on Exhibit A (including, without limitation, the right to
amend, terminate, supplement, and extend the Purchase Agreement, collectively
the "Contract Rights").

         2. ASSUMPTION. Each Assignee hereby agrees to assume and timely
perform all Contract Rights of the Assignor hereby sold, assigned, transferred,
and conveyed to such Assignee. Except as expressly set forth in this
Assignment, Assignees do not hereby assume or agree to pay any other
liabilities or obligations of Assignor of any nature whatsoever.

         3. TITLE TO CONTRACT RIGHTS. Assignor hereby binds itself, its
successors, and assigns to warrant and forever defend, all and singular, title
to the Contract Rights unto Assignees and their respective successors and
assigns against every person lawfully claiming or to claim the same or any part
thereof. Assignor warrants to each Assignee that it is conveying good title to
the Contract Rights free and clear of all Liens.

         4. POWER OF ATTORNEY. Assignor hereby constitutes and appoints each
Assignee as Assignor's true and lawful attorney, with full power of
substitution, for it and in its name, place, and stead, but on behalf of and
for the benefit of such Assignee, to demand and receive from time to time any
and all Contract Rights and to get receipts and releases for and in respect of
the same or any part thereof and to do all and any such acts and things in
relation thereto as such Assignee shall deem advisable.

         5. FURTHER ASSURANCES. Assignor, for itself and its successors and
assigns, hereby covenants and agrees with Assignees that Assignor will do,
execute, acknowledge, and deliver, or will cause to be done, executed,
acknowledged, and delivered, all such further acts, conveyances, transfers,
assignments, powers of attorney, and assurances that may be required to assure,
convey, transfer, confirm, and vest unto Assignees any and all of the Contract
Rights and to aid and assist Assignees in collecting and reducing the Contract
Rights to possession.

         6. GOVERNING LAW. This Assignment shall be governed by and construed
in accordance with the laws of the State of New York.


              [THE REMAINDER OF THIS PAGE IS INTENTIONALLY BLANK]



                                      2
<PAGE>   3

         IN WITNESS WHEREOF, the undersigned have caused this Agreement to be
signed, all as of the date first written above.

                                         ASSIGNOR:

                                         HMTF BRIDGE GLOBIX, LLC


                                         By: /s/ David W. Knickel
                                            -----------------------------------
                                         Name: David W. Knickel
                                              ---------------------------------
                                         Title: Vice President
                                               --------------------------------


                                         ASSIGNEES:

                                         HM4 GLOBIX QUALIFIED FUND, LLC


                                         By: /s/ David W. Knickel
                                            -----------------------------------
                                         Name: David W. Knickel
                                              ---------------------------------
                                         Title: Vice President
                                               --------------------------------



                                         HM4 GLOBIX PRIVATE FUND, LLC

                                         By: /s/ David W. Knickel
                                            -----------------------------------
                                         Name: David W. Knickel
                                              ---------------------------------
                                         Title: Vice President
                                               --------------------------------


                  [SIGNATURE PAGE TO ASSIGNMENT OF SECURITIES]

                                      S-1
<PAGE>   4

                                         HM PG-IV GLOBIX, LLC

                                         By: /s/ David W. Knickel
                                            -----------------------------------
                                         Name: David W. Knickel
                                              ---------------------------------
                                         Title: Vice President
                                               --------------------------------


                                         HM 4-SBS GLOBIX COINVESTORS, LLC

                                         By: /s/ David W. Knickel
                                            -----------------------------------
                                         Name: David W. Knickel
                                              ---------------------------------
                                         Title: Vice President
                                               --------------------------------


                                         HM 4-EQ GLOBIX COINVESTORS, LLC

                                         By: /s/ David W. Knickel
                                            -----------------------------------
                                         Name: David W. Knickel
                                              ---------------------------------
                                         Title: Vice President
                                               --------------------------------



                 [SIGNATURE PAGE TO ASSIGNMENT OF SECURITIES]

                                      S-2
<PAGE>   5

                                   EXHIBIT A

                            ASSIGNMENT OF SECURITIES

<TABLE>
<CAPTION>
                                                         SHARES OF SERIES A 7.5%
                                                              CONVERTIBLE
                                       PERCENTAGE           PREFERRED STOCK
          ASSIGNEE                     TRANSFERRED           TO BE ACQUIRED
--------------------------------      ------------           --------------
<S>                                       <C>                      <C>
HM4 Globix Qualified Fund, LLC          90.805306%                 18,161

HM4 Globix Private Fund, LLC             0.643298%                    129

HM PG-IV Globix, LLC                     4.834331%                    967

HM 4-SBS Globix Coinvestors, LLC         2.232843%                    447

HM 4-EQ Globix Coinvestors, LLC          1.484222%                    296
--------------------------------      -----------            ------------
Total                                    100.0000%                 20,000
                                      ===========            ============
</TABLE>