<PAGE>
EXHIBIT 4.1

THIS WARRANT AND ANY SECURITIES ACQUIRED UPON EXERCISE OF THIS WARRANT HAVE NOT
BEEN REGISTERED UNDER THE SECURITIES ACT OF 1933, AS AMENDED (THE "SECURITIES
ACT"), OR THE SECURITIES LAWS OF ANY STATE. NEITHER THIS WARRANT, SUCH
SECURITIES NOR ANY INTEREST THEREIN MAY BE TRANSFERRED EXCEPT PURSUANT TO AN
EFFECTIVE REGISTRATION STATEMENT UNDER THE SECURITIES ACT AND APPLICABLE STATE
SECURITIES LAWS OR PURSUANT TO AN APPLICABLE EXEMPTION FROM THE REGISTRATION
REQUIREMENTS OF THE SECURITIES ACT AND SUCH STATE SECURITIES LAWS.

                               GLOBIX CORPORATION

                   WARRANT TO PURCHASE SHARES OF COMMON STOCK

                 _____________________________________________

                                                             As of March 7, 2005



                  This warrant (this "WARRANT") certifies that, for good and
valuable consideration, Globix Corporation, a Delaware corporation (the
"COMPANY"), grants to [INSERT HOLDER] or its permitted assigns (the
"WARRANTHOLDER"), the right to subscribe for and purchase from the Company, at
any time during the Exercise Period (as defined herein), ____________ (______)
[INSERT NUMBER OF SHARES] shares of the Common Stock, par value $0.01 of the
Company (the "WARRANT SHARES"), at the exercise price per share of $_____
[INSERT EXERCISE PRICE] (the "EXERCISE PRICE"), all subject to the terms,
conditions and adjustments herein set forth. The number of Warrant Shares is
subject to adjustment as provided in ARTICLE III.

                  This Warrant is being issued in replacement of the
Warrantholder's warrant (the "ORIGINAL WARRANT") for the purchase of shares of
NEON Communications, Inc. ("NEON") as converted pursuant to the terms of that
certain Agreement and Plan of Merger, dated _________, 2004, between the Company
and NEON. By its acceptance of this Warrant, the Warrantholder acknowledges the
replacement and termination of the Original Warrant.

1.       DEFINITIONS

         1.1. DEFINITIONS. As used herein, unless the context otherwise
requires, the following terms have the following respective meanings:

         "AFFILIATE" with respect to any Person, shall mean any other Person
that directly or indirectly, controls, is controlled by, or is under common
control with, such Person.

         "BUSINESS DAY" means any day other than a Saturday, Sunday or a day on
which national banks are authorized by law to close in the State of New York.

         "CLOSING PRICE" of a share of Common Stock for any day shall mean the
last reported sales price, regular way, or, in the event that no sale takes
place on such day, the average of the reported closing bid and asked prices,
regular way, in either case as reported on the principal national securities
exchange on which such Common Stock is listed or admitted to trading or, if not
listed or admitted to trading on any national securities exchange, on the Nasdaq

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National Market System or the Nasdaq SmallCap Market or, if such security is not
quoted on the Nasdaq National Market System or the Nasdaq SmallCap Market, the
average of the closing bid and asked prices on each such day in the
over-the-counter market as reported by Nasdaq or, if bid and asked prices for
such security on each such day shall not have been reported by Nasdaq, the
average of the bid and asked prices for such day as furnished by any reputable
investment banking firm regularly making a market in such security selected for
such purpose by the Board of Directors of the Company or a committee thereof. If
the Closing Price cannot be calculated on such date on any of the foregoing
bases, the Closing Price of such security on such date shall be the fair market
value as reasonably determined by an Independent Financial Expert selected for
such purpose by the Board of Directors of the Company or a committee thereof.
For the purpose of this Warrant, and as appropriate, the Closing Price shall be
determined by the average of the closing prices for the five (5) trading days
prior to the date of the notice of exercise.

         "COMMON STOCK" means the common stock, par value $0.01 per share, of
the Company.

         "EXCHANGE ACT" means the Securities Exchange Act of 1934, as amended
from time to time.

         "GOVERNMENTAL AUTHORITY" means any foreign, federal, state, local or
other governmental authority or regulatory body having jurisdiction over the
Company, its Affiliates or the Warrantholder.

         "INDEPENDENT FINANCIAL EXPERT" means a nationally recognized investment
banking firm that does not (and whose directors, officers, employees and
Affiliates do not) have a direct or indirect financial interest in the Company
or any of its Affiliates, that has not been and at the time it is called upon to
give independent financial advice to the Company is not (and none of whose
directors, officers, employees or Affiliates is) a promoter, director or officer
of the Company or any of its Affiliates, and that does not provide any advice or
opinions to the Company or any of its Affiliates.

         "PERSON" means any individual, firm, corporation, partnership, limited
liability company, trust, incorporated or unincorporated association, joint
venture, joint stock company, Governmental Authority or other entity of any
kind, and shall include any successor (by merger or otherwise) of such entity.

         "SECURITIES ACT" means the Securities Act of 1933, as amended from time
to time.

II.      EXERCISE OF WARRANT

         2.1. EXERCISE PERIOD. On the terms and subject to the conditions
contained herein, the Warrantholder may exercise this Warrant on any Business
Day starting on _______ __, 200_ and ending at 5:00 p.m., Eastern Standard Time,
on _______ __, 200_ [INCORPORATE PERIOD FROM CONVERTED NEON WARRANT] (the
"EXERCISE PERIOD"), for all or any part of the Warrant Shares.

         2.2. EXERCISE PROCEDURE. To exercise this Warrant, the Warrantholder
shall deliver to the Company at its principal executive offices: (a) payment of
the aggregate Exercise Price in the manner provided in SECTION 2.3 (as computed
by multiplying (A) the Exercise Price by (B) the number of shares of Common
Stock for which the Warrantholder is exercising this Warrant at such time); (b)
a completed and properly executed Notice of Exercise in substantially the form
attached hereto as Annex I; and (c) this Warrant. The minimum number of shares


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of Common Stock for which this Warrant or any portion thereof shall be
exercisable at any one time shall be 10,000, unless the remaining number of
shares of Common Stock for which this Warrant is then exercisable shall be less
than 10,000, in which case such remaining shares shall be the minimum number of
shares of Common Stock for which this Warrant is then exercisable. Upon receipt
of the aggregate Exercise Price and the required deliverables pursuant to the
preceding sentence, the Company shall, within five (5) Business Days thereafter,
subject to receipt of any required regulatory approvals (including expiration of
any required waiting period), deliver to the Warrantholder duly executed
certificate(s) representing the aggregate number of shares of Common Stock
issuable upon such exercise, together with cash in lieu of any fraction of a
Warrant Share as provided in SECTION 2.6. Such stock certificate(s) shall be in
such denominations and registered in the name(s) as the Warrantholder shall
request in the Notice of Exercise. If this Warrant shall have been exercised in
part, the Company shall deliver to the Warrantholder a new warrant evidencing
the rights of the Warrantholder to purchase the remaining Warrant Shares
issuable (which shall in all other respects be identical to this Warrant). All
shares of Common Stock issuable upon the exercise of this Warrant pursuant to
the terms hereof shall be validly issued, fully paid and nonassessable and
without any preemptive rights.

         2.3. PAYMENT OF EXERCISE PRICE. The aggregate Exercise Price (computed
in the manner provided in Section 2.2) may be payable hereunder by the delivery
by certified check or by wire transfer of immediately available funds to the
account of the Company of an amount equal to the aggregate Exercise Price or by
instructing the Company to withhold from the shares of Common Stock to be issued
upon exercise of the Warrant a number of whole or fractional shares of Common
Stock equal to (i) the Exercise Price divided by the Closing Price of a share of
Common Stock ( as of the date of the Notice of Exercise) multiplied by (ii) the
number of shares of Common Stock for which the Warrantholder is exercising this
Warrant at such time.

         2.4. RESTRICTIONS. The Company shall not be required to issue any
shares of Common Stock under this Warrant if the issuance of such shares would
constitute a violation by the Company of any provision of any law, rule or
regulation of (i) any Governmental Authority, including without limitation,
compliance with the Hart-Scott-Rodino Antitrust Improvements Act of 1976, as
amended (the "HSR ACT"), and compliance with registration or qualification
requirements of applicable federal and state securities laws or (ii) any
applicable self governing organization or stock exchange, including without
limitation, the rules, regulations or listing requirements of any such
organization or stock exchange. If at any time the Company shall determine,
based upon the advice of counsel, that the registration, qualification or
listing of any shares subject to this Warrant under any applicable state or
federal law or other applicable rules or regulations (including those of any
applicable stock exchange), or any filing or expiration of any waiting period
under the HSR Act, is necessary as a condition of, or in connection with, the
issuance of shares, the Company shall not be required to issue any shares of
Common Stock under this Warrant unless and until the Company has received
evidence reasonably satisfactory to it that such laws, rules or regulations have
been complied with and/or such filing has been made and the applicable waiting
period has expired under the HSR Act; provided, however, that nothing in this
SECTION 2.4 shall limit the Company's obligations under ARTICLE V of this
Warrant.

         2.5. PAYMENT OF TAXES. The Company shall pay all stamp taxes and other
similar charges with respect to the issue or delivery of Common Stock hereunder.
The Company shall not be required to pay any transfer tax or other similar
charge imposed in connection with the issue of any stock certificate in any name
other than that of the Warrantholder, and in such case the Company shall not be
required to issue or deliver any stock certificate until such tax or other
charge has been paid or it has been established to the reasonable satisfaction
of the Company that no such tax or other charge is due. The Company shall be
entitled to deduct and withhold from amounts otherwise payable pursuant to this
Warrant to any Warrantholder such amounts as the Company is required to deduct
and withhold with respect to the making of such payment under the Internal
Revenue Code of 1986, as amended or under any provision of state, local or
foreign tax law. To the extent that amounts are so withheld by the Company, such
withheld amounts shall be treated for all purposes of this Warrant as having
been paid to the Warrantholder in respect of which such deduction and
withholding was made by the Company.

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         2.6. FRACTIONAL SHARES. The Company shall not be required to issue any
fractional shares of Common Stock upon exercise of this Warrant. In lieu of any
fractional share to which the Warrantholder would otherwise be entitled upon
exercise of this Warrant, the Company shall make a cash payment in an amount
equal to the product of (a) the Closing Price per share of Common Stock on the
date of the notice of exercise multiplied by (b) the fraction of a share.

III.     ADJUSTMENTS

         3.1. SUBDIVISION OR COMBINATION OF COMMON STOCK. If the Company at any
time subdivides (by any stock split, stock dividend, recapitalization or
otherwise) its outstanding shares of Common Stock into a greater number of
shares, then as of the record date for effecting such subdivision the number of
shares issuable upon exercise of this Warrant will be proportionately increased
and the Exercise Price in effect immediately prior to such subdivision shall be
proportionately decreased. If the Company at any time combines (by reverse stock
split, recapitalization or otherwise) its outstanding shares of Common Stock
into a smaller number of shares, then as of the record date for effecting such
combination the number of shares issuable upon exercise of this Warrant will be
proportionately decreased and the Exercise Price in effect immediately prior to
such combination shall be proportionately increased.

         3.2. CONSOLIDATION, MERGER, ETC. In case of any consolidation or merger
of the Company with or into any other corporation, entity or person, or (a) any
other corporate reorganization, in which the Company shall not be the continuing
or surviving entity of such consolidation, merger or reorganization or in
connection with which the Common Stock (or other securities issuable upon
exercise of this Warrant) shall be changed into or exchanged for stock of any
other entity or cash or other property, (b) any transaction in which in excess
of 50% of the Company's voting power is transferred to a person not a
stockholder immediately prior to the consummation of such transaction, (c) any
sale of all or substantially all of the assets of the Company or (d) a capital
reorganization or reclassification of the Common Stock (or other securities
issuable upon exercise of this Warrant) that does not result in an adjustment
pursuant to SECTION 3.1 (any such transaction being hereinafter referred to as a
"REORGANIZATION"), then, in each case, the Warrantholder, on exercise hereof at
any time after the consummation or effective date of such Reorganization, shall
receive, in lieu of the Warrant Shares issuable on such exercise prior to the
date of such Reorganization, the stock, other securities, cash or other property
to which such holder would have been entitled upon the date of such
Reorganization if such holder had exercised this Warrant immediately prior
thereto.

         3.3. NOTICE OF ADJUSTMENT. Whenever an event necessitating an
adjustment to this Warrant pursuant to this ARTICLE III occurs, the Company
shall promptly deliver written notice thereof, by first class mail, postage
prepaid, addressed to the Warrantholder in accordance with SECTION 7.5, which
notice shall state the increase or decrease in the number or other denominations
of securities purchasable and exercise price payable upon the exercise of this
Warrant setting forth in reasonable detail the method of calculation and the
facts upon which such calculation is based.


OBJECTION: IV.      RESTRICTIONS ON TRANSFER
--------------------------------------------

         4.1. RESTRICTIONS ON TRANSFER. The Warrantholder, by its acceptance of
this Warrant, agrees to be bound by the provisions of this ARTICLE IV and
acknowledges and confirms that this Warrant and any Warrant Shares issued upon
exercise of this Warrant have not been registered under the Securities Act or
any applicable state securities laws, and may not be sold or transferred except


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in compliance with and subject to the Securities Act and such state securities
laws. Unless and until this Warrant and such Warrant Shares have been registered
under the Securities Act and such state securities laws, the Company may
require, as a condition to effecting any sale or transfer of this Warrant or
such Warrant Shares on the books of the Company, an opinion of counsel
reasonably satisfactory to the Company to the effect that an exemption from
registration under the Securities Act and such state securities laws is
available for the proposed transfer or assignment or a certification reasonably
satisfactory to the counsel of the Company in its professional determination
from the transferee that it is an "ACCREDITED INVESTOR" as defined under the
Securities Act and regulations promulgated thereunder. Any purported sale or
transfer of this Warrant and/or such Warrant Shares shall be null and void
unless made in compliance with the conditions set forth in this ARTICLE IV.
Except as provided in SECTION 4.2, (a) this Warrant and any warrant of the
Company issued in exchange or replacement for this Warrant shall be stamped or
otherwise imprinted with a legend in substantially the form set forth on the
cover of this Warrant, (b) each stock certificate for Warrant Shares issued upon
the exercise of this Warrant and each stock certificate issued upon the transfer
of any such Warrant Shares shall be stamped or otherwise imprinted with a legend
substantially to the same effect.

         4.2. TERMINATION OF RESTRICTIONS. The restrictions imposed by SECTION
4.1 upon the transferability of this Warrant and the Warrant Shares shall
terminate: (a) when and so long as this Warrant or any such Warrant Shares shall
have been effectively registered under the Securities Act and transferred in
compliance therewith; or (b) when the Company shall have received an opinion of
counsel reasonably satisfactory to it that this Warrant or such Warrant Shares
may be transferred without registration thereof under the Securities Act;
provided, however, that if the Warrant Shares have been held (both legally and
beneficially) by the Warrantholder for at least one (1) year and are proposed to
be sold in compliance with Rule 144 under the Securities Act, no such opinion of
counsel shall be required. Whenever the legend requirements imposed by SECTION
4.1 shall terminate as to this Warrant or the Warrant Shares, the holder of this
Warrant or any Warrant Shares shall be entitled to receive from the Company, at
the Company's expense, a new warrant or a new stock certificate representing the
Warrant Shares, as the case may be, not bearing the restrictive legend described
in SECTION 4.1.

         4.3. COMPLIANCE WITH SECURITIES LAWS. The Warrantholder, by acceptance
hereof, represents to the Company that this Warrant and any Warrant Shares
purchased upon exercise of this Warrant are being acquired solely for the
Warrantholder's own account and not as a nominee for any other party, and for
investment, and that the Warrantholder will not offer, sell or otherwise dispose
of this Warrant or any such Warrant Shares except under circumstances that will
not result in a violation of the Securities Act or any applicable state
securities laws.

         4.4. TRANSFER PROCEDURE. Subject to compliance with the other
provisions of this ARTICLE IV, transfer of this Warrant, in whole or in part,
shall occur upon surrender of this Warrant at the principal executive offices of
the Company, together with a duly executed written assignment of this Warrant
and funds sufficient to pay any transfer taxes payable upon the making of such
transfer and, if required, an opinion of counsel reasonably acceptable to
counsel of the Company in its professional determination concerning the
compliance of such transfer with the Securities Act and applicable state
securities laws. Upon receipt of such items, the Company shall execute and
deliver a new warrant or warrants in the name of the assignee or assignees and
in the denomination(s) specified in such instrument of assignment, and shall
issue to the assignor a new warrant evidencing the portion of this Warrant not
so assigned, and this Warrant shall promptly be cancelled.

         4.5. MAINTENANCE OF TRANSFER BOOKS. The Company agrees to maintain, at
the principal executive office of the Company, books or records for the
registration and the registration of transfer of this Warrant or any warrant of
the Company issued in exchange for this Warrant.

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V.       NECESSARY ACTIONS

         The Company will: (a) use its reasonable best efforts to obtain all
such authorizations, approvals, exemptions or consents from any Governmental
Authority having jurisdiction thereof as may be necessary to enable the Company
to perform its obligations under this Warrant (including, without limitation,
making all necessary filings with such Governmental Authorities); (b) take all
necessary steps (including, without limitation, making appropriate amendments to
its certificate of incorporation) to ensure that the Company has authorized a
sufficient number of authorized but unissued shares of Common Stock to provide
for the issuance of the Warrant Shares; (c) reserve from such authorized but
unissued shares of common stock and keep available for issuance pursuant to this
Warrant a sufficient number of shares of Common Stock to provide for the
issuance of the Warrant Shares upon the exercise of this Warrant; (d) if and so
long as any shares of Common Stock are listed on a national securities exchange,
if permitted by the rules of such exchange, list and keep listed on such
exchange, upon official notice of issuance, all shares of Common Stock issuable
upon exercise of this Warrant; and (d) take all actions as may be necessary or
appropriate to ensure that the Company may validly and legally issue fully paid
and non-assessable shares of Common Stock upon the exercise of this Warrant that
are not subject to any preemptive rights and are free from all taxes, liens,
security interests, charges, and other encumbrances with respect to the issuance
thereof, other than taxes in respect of any transfer occurring contemporaneously
with such issuance. If the Company determines that registration of the Warrant
Shares under any federal or state securities law or any other governmental
approval is required prior to the issuance of the Warrant Shares, then the
Company shall use its reasonable best efforts to secure such registration or
approval, and the right to exercise this Warrant shall be extended until 15 days
after the completion of any such registration or approval.

VI.      LOSS OR MUTILATION

         On receipt of evidence reasonably satisfactory to the Company of the
loss, theft, destruction or mutilation of this Warrant and (a) in the case of
loss, theft or destruction, on delivery of an indemnity agreement reasonably
satisfactory in form and substance to the Company; or (b) in the case of
mutilation, on surrender and cancellation of this Warrant, the Company shall
execute and deliver, in lieu of this Warrant, a new warrant of like tenor and
amount.

VII.     MISCELLANEOUS

         7.1 ENTIRE AGREEMENT. This Warrant constitutes the entire agreement
between the Company and the Warrantholder with respect to the Warrant.

         7.2 NONWAIVER. No course of dealing or any delay or failure to exercise
any right hereunder on the part of the Warrantholder shall operate as a waiver
of such right or otherwise prejudice the Warrantholder's rights, powers or
remedies.

         7.3 BINDING EFFECT; NO THIRD-PARTY BENEFICIARIES. This Warrant shall
inure to the benefit of and shall be binding upon the Company and the
Warrantholder and their respective successors and permitted assigns. Nothing in
this Warrant, expressed or implied, is intended to or shall confer on any person
other than the Company and the Warrantholder, or their respective successors or
permitted assigns, any rights, remedies, obligations or liabilities under or by
reason of this Warrant.

         7.4 SECTION AND OTHER HEADINGS. The section and other headings
contained in this Warrant are for reference purposes only and shall not be
deemed to be a part of this Warrant or to affect the meaning or interpretation
of this Warrant.

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         7.5 NOTICES. Except as otherwise expressly provided herein, all notices
and deliveries referred to in this Warrant shall be in writing (including
facsimile transmission or similar writing) and shall be given to such party at
its address or facsimile number set forth on the signature pages hereof. Each
such notice, request or other communication shall be deemed received by the
other party (i) if given by facsimile transmission, when transmitted to the
facsimile number specified in this Section 7.5 and confirmation of receipt is
received, (ii) if given by mail, 72 hours after such communication is deposited
in the mails with first class postage prepaid, addressed as aforesaid or (iii)
if given by any other means, when delivered at the address specified in this
Section 7.5.

         7.6 SEVERABILITY. Whenever possible, each provision of this Warrant
will be interpreted in such manner as to be effective and valid under applicable
law, but if any provision of this Warrant is held by a court of competent
jurisdiction to be invalid, illegal or unenforceable in any respect under any
applicable law or rule in any jurisdiction, such invalidity, illegality or
unenforceability will not affect any other provision of this Warrant or the
validity, legality or enforceability of this Warrant in any other jurisdiction.
In such event, this Warrant will be reformed, construed and enforced in such
jurisdiction as if such invalid, illegal or unenforceable provision had never
been contained herein.

         7.7 GOVERNING LAW. All questions concerning the construction, validity
and interpretation of this warrant and the issuance of securities hereunder will
be governed by and construed in accordance with the internal laws of the State
of Delaware, without giving effect to any choice of law or conflict of law
provision or rule (whether of the State of Delaware or any other jurisdiction)
that would cause the application of the laws of any jurisdiction other than the
State of Delaware.

         7.8 RIGHTS OR LIABILITIES AS STOCKHOLDER. The Warrantholder shall be
deemed to have become a holder of record of the shares of Common Stock issuable
under SECTION 2.2 as of the date on which all required deliverables pursuant to
SECTION 2.2 have been received by the Company. Until such time the Warrantholder
shall not have any voting rights or other rights or liabilities of a stockholder
of the Company with respect to the Common Stock issuable hereunder.

         7.9 AMENDMENT. No amendment or waiver of any provision of this Warrant
shall be effective without the prior written consent of the Company and the
Warrantholder.

         IN WITNESS WHEREOF, the Company has caused this Warrant to be signed by
its duly authorized officer.

                                            GLOBIX CORPORATION



                                            By:      _________________________
                                            Name:    _________________________
                                            Title:   _________________________



                                            Warrantholder Information:

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