<PAGE>

                                                                    EXHIBIT 4.11

                         SUBSIDIARY SECURITY AGREEMENT
                             (LOCAL FIBER, L.L.C.)

     This SUBSIDIARY SECURITY AGREEMENT (as amended, supplemented, amended and
restated or otherwise modified from time to time, this "Security Agreement"), is
entered into as of April 11, 2000 by LOCAL FIBER, L.L.C., a New York limited
liability company (the "Grantor"), in favor of DEUTSCHE BANK AG NEW YORK BRANCH,
as administrative agent (together with any successor(s) thereto in such
capacity, the "Administrative Agent") for each of the Secured Parties.

                                   RECITALS
                                   --------

     A.  Pursuant to the Credit Agreement, dated as of April 11, 2000 (as
amended, supplemented, amended and restated or otherwise modified from time to
time, the "Credit Agreement"), among FiberNet Telecom Group, Inc., a Delaware
corporation (the "Borrower"), the financial institutions from time to time
parties thereto as Lenders (collectively, the "Lenders"), the Administrative
Agent, Deutsche Bank Securities Inc., as co-syndications agent, and Toronto
Dominion (Texas), Inc., as co-syndications agent, the Lenders have extended
commitments to make Loans or issue Letters of Credit (each as defined in the
Credit Agreement) to, and for the benefit of, the Borrower;

     B.  It is a condition precedent to the effectiveness of the Credit
Agreement that the Grantor execute this Security Agreement;

     C.  The Grantor has duly authorized the execution, delivery and performance
of this Security Agreement; and

     D.  It is in the best interests of the Grantor to execute this Security
Agreement as the Grantor will derive substantial direct and indirect benefits
from the Loans made to the Borrower, and the Letters of Credit issued for the
benefit of the Borrower, by the Lenders from time to time pursuant to the Credit
Agreement.

                                   AGREEMENT
                                   ---------

     For good and valuable consideration, the receipt and sufficiency of which
are hereby acknowledged, and in order to induce the Lenders to make Loans and
issue Letters of Credit to or for the benefit of the Borrower pursuant to the
Credit Agreement, and to induce the Secured Parties to enter into any Interest
Rate Agreements, the Grantor agrees, for the benefit of each Secured Party, as
follows:
<PAGE>

ARTICLE I.
                                  DEFINITIONS

     Section 1.1  Defined Terms.
                  --------------

     The following terms when used in this Security Agreement shall have the
following meanings:

          "Administrative Agent" shall have the meaning set forth in the
preamble.
--------

          "Borrower" shall have the meaning set forth in the first recital.
                                                             --------------

          "Collateral" shall have the meaning set forth in Section 2.1.
                                                           -----------

          "Credit Agreement" shall have the meaning set forth in the first
                                                                     -----
recital.
-------

          "Grantor" shall have the meaning set forth in the preamble.
                                                            --------

          "Lenders" shall have the meaning set forth in the first recital.
                                                            -------------

          "Permits" shall have the meaning set forth in Section 2.1.
                                                        -----------

          "Receivables" shall have the meaning set forth in Section 2.1.
                                                            -----------

          "Related Contracts" shall have the meaning set forth in Section 2.1.
                                                                  -----------

          "Security Agreement" shall have the meaning set forth in the preamble.
                                                                       --------

     Section 1.2  Credit Agreement Definitions; Principles of Interpretation.
                  -----------------------------------------------------------

     Unless otherwise defined herein or unless the context otherwise requires,
terms used in this Security Agreement, including its preamble and recitals, have
the meanings provided in the Credit Agreement (including the principles of
interpretation set forth in Section 1.3 of the Credit Agreement).  All
                            -----------
references herein to the security interest granted to, assignment or pledge to
or other rights or interests granted hereby to the Administrative Agent shall be
deemed to be rights or interests granted to the Administrative Agent for the
benefit of each of the Secured Parties, whether or not specifically so stated.

     Section 1.3  UCC Definitions.
                  ----------------

     Unless otherwise defined herein or in the Credit Agreement or unless the
context otherwise requires, terms for which meanings are provided in the UCC are
used in this Security Agreement, including its preamble and recitals, with such
meanings.

                                       2
<PAGE>

                                  ARTICLE II.


     Section 2.1  Creation of Security Interest.
                  ------------------------------

     As security for the due and punctual payment in full in cash and
performance in full of the Obligations, the Grantor hereby assigns and pledges
to the Administrative Agent for the benefit of the Secured Parties, and grants
to the Administrative Agent for the benefit of the Secured Parties a security
interest in and lien on, all of the Grantor's right, title and interest in and
to the following, whether now owned or hereafter existing or acquired by the
Grantor (collectively, the "Collateral"):

                  (a) all "accounts" (as defined in the UCC), contracts
          (including the Contracts) and rights (including (i) rights of the
          Grantor to receive moneys due and to become due under or pursuant to
          any contract (whether as contractual obligations, damages or
          otherwise), (ii) all rights of the Grantor to receive any proceeds of
          any insurance, indemnity, warranty, or guarantee with respect to any
          contract, (iii) all rights of the Grantor with respect to claims,
          rights, powers, or privileges under any contract, (iv) all rights of
          the Grantor to terminate, amend, supplement or modify any contract, to
          perform thereunder and to compel performance and otherwise exercise
          all remedies thereunder, (v) all rights of the Grantor under each
          contract to make determinations, to exercise any election (including,
          but not limited to, the election of remedies) or option or to give or
          receive any notice, consent, waiver, or approval, together with full
          power and authority with respect to any contract to demand, receive,
          enforce, collect or provide receipt for any of the foregoing rights or
          any property the subject of any of the contracts, to enforce or
          execute any checks, or other instruments or orders, to file any claims
          and to take any action which may be necessary or advisable in
          connection with any of the foregoing, and (vi) the rights of the
          Grantor to payment for goods or other property (including, the sale of
          capacity or any other use of the System or a portion thereof) sold or
          leased or services performed by the Grantor) (the "Contracts"),
          chattel paper, documents, and instruments of the Grantor, in all cases
          whether or not arising out of or in connection with the sale or lease
          of goods or the rendering of services, and all of the Grantor's right,
          title and interest in and to any goods, services or property
          represented by the foregoing prior to the sale thereof, and all rights
          of the Grantor now or hereafter existing in and to all security
          agreements, guaranties, leases, letters of credit, guarantees and
          other contracts securing or otherwise relating to any such accounts,
          contracts, contract rights, chattel paper, documents, and instruments
          (any and all such accounts, contracts, contract rights, chattel paper,
          documents and instruments being the "Receivables," and any and all
          such security agreements, guaranties, leases and other contracts being
          the "Related Contracts");

                                       3
<PAGE>

                  (b) all "general intangibles" (as defined in the UCC),
          including, to the extent assignable, all rights relating to design,
          development, operation, and use of the System, all certificates of
          occupancy, zoning variances, building, use or other permits,
          approvals, authorizations, licenses and consents obtained from any
          governmental agency in connection with the development, use, operation
          or management of the System (the "Permits"), all construction,
          service, engineering, consulting, architectural and other similar
          contracts concerning the design, construction, operation, occupancy
          and/or use of the System, all architectural drawings, plans,
          specifications, soil tests, appraisals, route surveys, engineering
          reports and similar materials relating to all or any portion of the
          System, and all payment and performance bonds or warranties or
          guarantees relating to the System; all rights under and in patents,
          patent licenses, rights in intellectual property, trademarks, trade
          names, corporate names, company names, business names, fictitious
          business names, trade styles, trade secrets, service marks, logos,
          other source and business identifiers, trademark registrations and
          applications for registration used exclusively at or relating
          exclusively to any part of the Grantor's business; all renewals,
          extensions and continuations-in-part of the items referred to above;
          any written agreements granting to the Grantor any right to use any
          trademark or trademark registration at or in connection with the
          Grantor's business; and the right of the Grantor to sue for past,
          present and future infringements of the foregoing; and the right in
          the name and on behalf of the Grantor to appear in and defend any
          action or proceeding brought with respect to any part of the Grantor's
          real or personal property and to commence any action or proceeding to
          protect the interest of the Grantor in such Collateral;

                  (c) all books, records, writings, design documents, computer
          programs, printouts and other computer materials and records, data
          bases, software, information and other property relating to, used or
          useful in connection with, the Grantor's business;

                  (d) to the extent not otherwise included in any of the classes
          or categories enumerated above, all equipment, inventory, documents,
          instruments, securities and chattel paper (as each of such terms is
          defined in the UCC) relating to the Collateral;

                  (e) all personal property of whatever kind or nature
          whatsoever, including personal property used in the operation of the
          Grantor's business, or in any way related to the land on which the
          System is located, the System or any other improvements on such land,
          whether located on or in, affixed to, or attached to such land or
          improvements or otherwise related thereto or arising therefrom, and
          whether tangible or intangible, direct or indirect, fully matured or
          contingent, and all extensions, additions, improvements, betterments,
          renewals, substitutions, and replacements to or of any of the
          foregoing;

                                       4
<PAGE>

                  (f) to the extent not otherwise included in any of the
          foregoing classes or categories of personal property, all proceeds
          (including all proceeds as defined in the UCC and all cash and non-
          cash proceeds as referred to in Section 552 of the United States
          Bankruptcy Code), products, offspring and profits of or from any of
          the foregoing;

                  (g) all motor vehicles and all rights under equipment leases
          and all bills of lading and warehouse receipts relating to the
          Collateral; and

                  (h) any and all additions and accessions to the Collateral,
          and all proceeds thereof, including proceeds of the conversion,
          voluntary or involuntary, of any of the foregoing into cash or
          liquidated claims, including all awards, all insurance proceeds,
          including any unearned premiums or refunds of premiums on any
          insurance policies covering all or any part of the Collateral and the
          right to receive and apply the proceeds of any insurance, or of any
          judgments or settlements made in lieu thereof for damage to or
          diminution of the Collateral;

     provided, however, that with respect to the Contracts, any such Contract
shall only be deemed to be and treated as Collateral if (i) such Contract or
Related Contract (other than Receivables) may lawfully be assigned (whether as
an outright assignment or as collateral security) to the Administrative Agent,
for the benefit of the Secured Parties, and (ii) the granting of a security
interest in and lien on, all of the Grantor's right, title and interest in such
Contract or Related Contract (other than Receivables) will not conflict with,
result in a breach of or constitute (with due notice or lapse of time or both) a
default under such Contract or Related Contract (other than Receivables); and
provided, further, that with respect to the Permits, any such Permit shall only
be deemed to be and treated as Collateral if such Permit may lawfully be
assigned (whether as an outright assignment or as collateral security) to the
Administrative Agent, for the benefit of the Secured Parties.

     Section 2.2  Financing Statements.
                  ---------------------

     The Grantor shall execute all financing statements, continuation
statements, assignments, certificates, and other documents and instruments with
respect to the Collateral pursuant to the UCC and otherwise as may be necessary
or reasonably requested by the Administrative Agent to perfect or from time to
time to publish notice of, or continue or renew the security interests granted
hereby (including, such financing statements, continuation statements,
certificates, and other documents as may be necessary or reasonably requested to
perfect a security interest in any additional property or rights hereafter
acquired by the Grantor or in any replacements, products or proceeds thereof),
in each case in form and substance satisfactory to the Administrative Agent. The
Grantor will pay the cost of filing the same in all public offices where filing
is necessary or reasonably requested by the Administrative Agent and will pay
any and all recording, transfer or filing taxes that may be due in connection
with any such filing. The Grantor grants the Administrative Agent the right, at
any time and at the Administrative Agent's option, and at the Grantor's expense,
to file any or all such financing statements, continuation

                                       5
<PAGE>

statements, and other documents pursuant to the UCC and otherwise as the
Administrative Agent reasonably may deem necessary or desirable.

     Section 2.3  Injury to Collateral.
                  ---------------------

     No injury to, or loss or destruction of, the Collateral or any part thereof
shall relieve the Grantor of any of the Obligations.

     Section 2.4  Continuing Security Interest; Transfer of Notes.
                  ------------------------------------------------

     This Security Agreement shall create a continuing security interest in the
Collateral and shall

                  (a) remain in full force and effect until payment in full in
          cash of all Obligations, the termination of all Interest Rate
          Agreements to which any Secured Party is a party and the termination
          of all Commitments,

                  (b) be binding upon the Grantor, its successors, transferees
          and assigns, and

                  (c) inure, together with the rights and remedies of the
          Administrative Agent hereunder, to the benefit of the Administrative
          Agent and each other Secured Party.

Without limiting the generality of the foregoing clause (c), any Lender may
assign or otherwise transfer (in whole or in part) any Note, Loan or Commitment
held by it as well as any interest in any other Obligations to any other Person
or entity as permitted by, and  in accordance with the terms of the Credit
Agreement, and such other Person or entity shall thereupon become vested with
all the rights and benefits in respect thereof granted to such Lender under any
Loan Document (including this Security Agreement) or otherwise, subject,
however, to any contrary provisions in such assignment or transfer, and to the
provisions of Sections 9.1 and 9.16 of the Credit Agreement.
              ------------     ----

     Section 2.5  Grantor Remains Liable.
                  -----------------------

     Anything herein to the contrary notwithstanding:

                  (a) the Grantor shall remain liable under the contracts and
          agreements included in the Collateral to the extent set forth therein,
          and shall perform all of its duties and obligations under such
          contracts and agreements to the same extent as if this Security
          Agreement had not been executed,

                  (b) the exercise by the Administrative Agent of any of its
          rights hereunder shall not release the Grantor from any of its duties
          or obligations under any such contracts or agreements included in the
          Collateral, and

                                       6
<PAGE>

                  (c) neither the Administrative Agent nor any other Secured
          Party shall have any obligation or liability under any such contracts
          or agreements included in the Collateral by reason of this Security
          Agreement, nor shall the Administrative Agent or any other Secured
          Party be obligated to perform any of the obligations or duties of the
          Grantor thereunder or to take any action to collect or enforce any
          claim for payment assigned hereunder.

     Section 2.6   Security Interest Absolute.
                  ---------------------------

     All rights of the Administrative Agent and the security interests granted
to the Administrative Agent hereunder, and all obligations of the Grantor
hereunder, shall be absolute and unconditional irrespective of :

          (a) any lack of validity, legality or enforceability of the Credit
     Agreement, any Note, or any other Loan Document or any Interest Rate
     Agreement;

          (b) the failure of any Secured Party or any holder of any Note

                    (i) to assert any claim or demand or to enforce any right or
              remedy against the Borrower, any other Loan Party or any other
              Person (including any other grantor) under the provisions of the
              Credit Agreement, any Note, any other Loan Document, any Interest
              Rate Agreement or otherwise, or

                    (ii) to exercise any right or remedy against any other
              grantor of, or collateral securing, any of the Obligations;

          (c) any change in the time, manner or place of payment of, or in any
     other term of, all or any of the Obligations, or any other extension or
     renewal of any Obligation of the Borrower or any other Loan Party;

          (d) any reduction, limitation, impairment or termination of any of the
     Obligations for any reason other than the written agreement of the Secured
     Parties to terminate the Obligations in full, including any claim of
     waiver, release, surrender, alteration or compromise, and shall not be
     subject to, and the Grantor hereby waives any right to or claim of, any
     defense or setoff, counterclaim, recoupment or termination whatsoever by
     reason of the invalidity, illegality, nongenuineness, irregularity,
     compromise, unenforceability of, or any other event or occurrence
     affecting, any Obligations of the Borrower, any other Loan Party or
     otherwise;

          (e) any amendment to, rescission, waiver, or other modification of, or
     any consent to departure from, any of the terms of the Credit Agreement,
     any Note, any other Loan Document or any Interest Rate Agreement;

                                       7
<PAGE>

          (f) any addition, exchange, release, surrender or non-perfection of
     any collateral, or any amendment to or waiver or release or addition of, or
     consent to departure from, any other security interest held by any Secured
     Party or any holder of any Note securing any of the Obligations; or

          (g) any other circumstance which might otherwise constitute a defense
     available to, or a legal or equitable discharge of, the Borrower, any other
     Loan Party, any surety or any grantor.

     Section 2.7  Postponement of Subrogation.
                  ----------------------------

     The Grantor agrees that it will not exercise any rights which it may
acquire by way of rights of subrogation under this Security Agreement, by any
payment made hereunder or otherwise, until the prior payment in full in cash of
all of the Obligations, the termination of all Interest Rate Agreements to which
any Secured Party is a party and the termination of all Commitments.  Any amount
paid to the Grantor on account of any such subrogation rights prior to the
payment in full in cash of all of the Obligations shall be held in trust for the
benefit of the Secured Parties and each holder of a Note and shall immediately
be paid to the Administrative Agent for the benefit of the Secured Parties and
each holder of a Note and credited and applied against the Obligations of the
Borrower and each other Loan Party, whether matured or unmatured, such order as
the Administrative Agent shall elect; provided,  however, that if
                                      --------   -------

          (a) the Grantor has made payment to the Secured Parties and each
     holder of a Note of all or any part of the Obligations, and

          (b) all Obligations have been paid in full in cash, all Interest Rate
     Agreements to which any Secured Party is a party have been terminated and
     all Commitments have been permanently terminated,

then, at the Grantor's request, the Administrative Agent, on behalf of the
Secured Parties and the holders of the Notes, will execute and deliver to the
Grantor appropriate documents (without recourse and without representation or
warranty) necessary to evidence the transfer by subrogation to the Grantor of an
interest in the Obligations resulting from such payment by the Grantor.  In
furtherance of the foregoing, for so long as any Obligations or Commitments
remain outstanding, the Grantor shall refrain from taking any action or
commencing any proceeding against the Borrower or any other Loan Party (or any
of its or their successors or assigns, whether in connection with a bankruptcy
proceeding or otherwise) to recover any amounts in respect of payments made
under this Security Agreement to any Secured Party or any holder of a Note,
except that the Grantor may file a proof of claim in a bankruptcy proceeding
with respect to the Borrower or any other Loan Party in connection with any
obligations owed by such Loan Party to the Grantor in the event that the
Administrative Agent has failed to file a proof of claim on the Grantor's behalf
by the second business day before the due date for such filing.

                                       8
<PAGE>

                                 ARTICLE III.
                   REPRESENTATIONS AND WARRANTIES OF GRANTOR

     The Grantor hereby represents and warrants to the Administrative Agent and
the other Secured Parties that:

     Section 3.1  Title to Collateral.
                  --------------------

     The Grantor is the sole owner of, and has good, valid, and marketable title
to, the Collateral, free from all Liens other than Permitted Liens, and the
Grantor has full right and power to grant the Administrative Agent for the
benefit of the Secured Parties a lien thereon and a security interest therein.

     Section 3.2  Security Interest.
                  ------------------

     The execution and delivery of this Security Agreement creates a good and
valid lien on and security interest in the Collateral.

     Section 3.3  Negotiable Documents, Instruments and Chattel Paper.
                  ----------------------------------------------------

     The Grantor has, contemporaneously with the execution and delivery of this
Security Agreement, delivered to the Administrative Agent possession of all
originals of all negotiable documents, instruments and chattel paper, including
all negotiable documents, instruments and chattel paper evidencing Receivables,
currently owned or held by the Grantor (duly endorsed in blank, if requested by
the Administrative Agent).

     Section 3.4  Authorization, Approval, Etc.
                  -----------------------------

     Except as have been obtained or made and are in full force and effect, no
authorization, approval or other action by, and no notice to or filing with, any
Governmental Instrumentality, regulatory body or any other Person is required
for the grant by the Grantor of the security interest granted hereby or for the
execution, delivery and performance of this Security Agreement by the Grantor or
for the exercise by the Administrative Agent of the rights provided for in this
Security Agreement, other than those authorizations, approvals, actions, notices
or filings set forth in Schedule 3.4 hereto.
                        ------------

     Section 3.5  Bankruptcy Matters.
                  -------------------

     The Grantor has not made a general assignment for the benefit of creditors,
filed any voluntary petition in bankruptcy or suffered the filing of an
involuntary petition by its creditors, suffered the appointment of a receiver to
take possession of all or substantially all of its assets, suffered the
attachment or other judicial seizure of all or substantially all of its assets,
admitted its inability to pay its debts as they come due, or made an offer of
settlement, extension or composition to its creditors generally.

                                       9
<PAGE>

     Section 3.6  Representations and Warranties under the Credit Agreement.
                  ----------------------------------------------------------

     The representations and warranties of or pertaining to the Grantor
contained in the Credit Agreement and each of the other Loan Documents are true
and correct as of the date hereof to the same extent as if set forth in full
herein.

     Section 3.7  Location of Collateral.
                  -----------------------

     The Grantor's principal place of business and chief executive office is
located at 570 Lexington Avenue, New York, New York 10022.

                                  ARTICLE IV.
                             COVENANTS OF GRANTOR

     Section 4.1  General Covenants Relating to Collateral.
                  -----------------------------------------

     Until all Obligations have been paid and performed in full, all Commitments
have been terminated and all Interest Rate Agreements to which any Secured Party
is a party have been terminated, the Grantor hereby covenants that, unless the
Administrative Agent, acting pursuant to the Credit Agreement, otherwise
consents in advance in writing:

     Section 4.1.1  Collateral.
                    ----------

     The Grantor shall (a) execute and deliver any and all documents, or cause
the execution and delivery of any and all documents, necessary to create,
perfect, preserve, validate or otherwise protect the Administrative Agent's lien
on and security interest in the Collateral and the priority thereof, (b)
maintain, or cause to be maintained, at all times the Administrative Agent's
lien on and security interest in the Collateral and the priority thereof, (c)
promptly upon learning thereof, report to the Administrative Agent any matters
that could reasonably be expected to materially and adversely affect the value
or enforceability or collectibility of any of the Collateral, (d) defend the
Collateral and the Administrative Agent's interests therein against all claims
and demands of all persons at any time claiming the same or any interest therein
adverse to the Administrative Agent and pay all costs and expenses (including,
reasonable attorneys' fees and charges) incurred in connection with such
defense, and (e) at the Grantor's sole cost and expense, settle any and all such
claims and disputes and indemnify and protect the Administrative Agent against
any liability, loss, cost or expense (including, reasonable attorneys' fees and
charges), arising therefrom or out of any matter affecting any of the Collateral
(provided, however, that if the Administrative Agent shall so elect after the
 --------  -------
occurrence and during the continuation of an Event of Default hereunder, the
Administrative Agent shall have the right at all times to settle, compromise,
adjust or liquidate all claims or disputes directly with the Grantor or any
obligor of the Grantor upon such terms and conditions as the Administrative
Agent reasonably deems advisable, and to charge all costs and expenses thereof
(including, reasonable attorneys' fees and charges) to the Grantor's account and
to add them to the Obligations, whereupon such costs and expenses shall be and
become part of the Obligations).

                                       10
<PAGE>

     Section 4.1.2  No Change in Places of Business or Collateral.
                    ---------------------------------------------

     The Grantor shall (a) maintain its places of business and its chief
executive office only in the locations set forth in Section 3.7, and in such
                                                    -----------
other places as the Grantor may select, provided that the Grantor shall provide
to the Administrative Agent at least twenty (20) days' prior written notice of
any changes in or additions to the locations of the Grantor's places of business
or of the Grantor's principal office and shall make all filings in the
applicable jurisdictions necessary to maintain the Administrative Agent's lien
on and security interest in the Collateral and the priority thereof in
connection with any such changes or additions, (b) keep, store and maintain the
Collateral only at the foregoing locations, and (c) keep and maintain the
records and books of account relating to the Collateral only at the Grantor's
chief executive office.

     Section 4.1.3  No Impairment.
                    -------------

     The Grantor shall not take or permit to be taken any action in connection
with the Collateral which would impair in any material respect the value of the
interests or rights of the Grantor therein or which would impair the interests
or rights of the Administrative Agent therein or with respect thereto.

     Section 4.2  Sale of Assets.
                  ---------------

     Sell, lease, assign, pledge, transfer or otherwise dispose of any of the
Collateral, whether now owned or hereafter acquired, except as expressly
permitted by the Credit Agreement.

                                  ARTICLE V.
                RIGHTS AND REMEDIES OF THE ADMINISTRATIVE AGENT

     Section 5.1  Miscellaneous Rights of the Administrative Agent.
                  -------------------------------------------------

     Upon the occurrence and during the continuation of an Event of Default, the
Administrative Agent shall have the right: (i) to declare all of the monetary
Obligations to be immediately due and payable, whereupon all such Obligations
shall become immediately due and payable without presentment, demand, notice of
dishonor, protest or further notice of any kind, all of which are hereby
expressly waived by the Grantor, anything contained herein to the contrary
notwithstanding; (ii) to exercise any one or more of the rights and remedies
exercisable by the Administrative Agent under any other provisions of this
Security Agreement, or any other related agreement, or exercisable by a secured
party under the UCC or under any other applicable law; and (iii) to exercise, in
the name of the Grantor or in the name of the Administrative Agent, such rights
and powers with respect to the Collateral as the Grantor might exercise,
including, the right to:

                  (a) enter into any extension, reorganization, deposit, merger,
          consolidation or other agreement pertaining to, or deposit, surrender,
          accept, hold or apply other property in exchange for, the Collateral
          or any part thereof;

                                       11
<PAGE>

                  (b) insure, process, and preserve the Collateral;

                  (c) transfer the Collateral or any part thereof to the name of
          the Administrative Agent or to the name of the Administrative Agent's
          nominee;

                  (d) receive, open, and dispose of mail addressed to the
          Grantor relating to the Collateral or any part thereof;

                  (e) collect and endorse, receive, and give receipts for all
          dividends, interest, rent, payments, proceeds, and other sums and
          property now or hereafter payable on or on account of the Collateral
          or any part thereof or on account of its sale or lease;

                  (f) initiate, pursue, compromise, settle or withdraw any
          claims, suits or proceedings pertaining to the Collateral or any part
          thereof or to any interest, rent or other payment on or on account of
          the Collateral or any part thereof or on account of its sale or lease;

                  (g) take possession of and endorse in the name of the Grantor
          or in the name of the Administrative Agent, for the account of the
          Grantor, any bills of exchange, checks, drafts, money orders, notes or
          any other chattel paper, documents or instruments constituting all or
          any part of the Collateral or received as interest, rent or other
          payment on or on account of the Collateral or any part thereof or on
          account of its sale or lease;

                  (h) appoint another (who may be an employee, officer or other
          representative of the Administrative Agent) to do any of the foregoing
          on behalf of the Administrative Agent;

                  (i) execute (in the name, place and stead of the Grantor)
          endorsements, assignments and other instruments of conveyance or
          transfer with respect to all or any of the Collateral; and

                  (j) take any other action which the Administrative Agent deems
          necessary or desirable to protect or realize upon its security
          interest in the Collateral or any part thereof, and the Grantor hereby
          irrevocably appoints the Administrative Agent as the Grantor's
          attorney-in-fact to take any such action, including the execution and
          delivery of any and all documents or instruments related to the
          Collateral or any part thereof in the Grantor's name, and said
          appointment shall create in the Administrative Agent a power coupled
          with an interest which shall be irrevocable.

     Section 5.2 Right of the Administrative Agent to Take Possession and
                 --------------------------------------------------------
Foreclose.
----------

                                       12
<PAGE>

     Upon the occurrence and during the continuation of any Event of Default,
the Administrative Agent shall have the right and power to take possession of
the Collateral and of any and all books of account and records of the Grantor
relating to any of the Collateral, the right to place the Administrative Agent's
representatives upon any premises on which the Collateral or any part thereof or
any such books of account or records may be situated with full power to remove
the same therefrom, and the right to exclude the Grantor and all persons
claiming under the Grantor from any access to the Collateral or to any part
thereof, and the Administrative Agent and such representatives are hereby
granted the irrevocable license to enter upon such premises for such purpose.
The Administrative Agent may require the Grantor to assemble the Collateral or
any part thereof and to make the same (to the extent the same is moveable)
available to the Administrative Agent at a place to be designated by the
Administrative Agent which is reasonably convenient to the Grantor and the
Administrative Agent.  The Administrative Agent may render the Collateral or any
part thereof unusable without removing the same from the premises on which it
may be situated, and may sell the same on the premises of the Grantor if such
Collateral or part thereof is situated thereon.  The Administrative Agent may
make formal application for the transfer of all of the Grantor's permits,
licenses, approvals, and the like relating to the Collateral or to the Grantor's
business to the Administrative Agent or to any assignee of the Administrative
Agent or to any purchaser of any of the Collateral to the extent the same are
assignable in accordance with their terms and applicable law.  Unless the
Collateral is perishable or threatens to decline speedily in value or is of a
type customarily sold on a recognized market, the Administrative Agent will give
the Grantor at least ten (10) days' prior written notice of the time and place
of any public sale thereof or of the time after which any private sale or any
other intended disposition thereof is to be made, which notice shall constitute
reasonable notice.  In addition to exercising the foregoing rights, the
Administrative Agent may, to the extent permitted by law, arrange for and
conduct the sale of the Collateral at a public or private sale, as the
Administrative Agent may elect, which sale may be conducted by an employee or
representative of the Administrative Agent, and any such sale shall be
considered or deemed to be a sale made in a commercially reasonable manner.  The
Administrative Agent may release, temporarily or otherwise, to the Grantor any
item of Collateral of which the Administrative Agent has taken possession
pursuant to any right granted to the Administrative Agent by this Security
Agreement without waiving any rights granted to the Administrative Agent under
this Security Agreement, the Credit Agreement, or the other Loan Documents or
any other agreement related hereto or thereto.  The Grantor, in dealing with or
disposing of the Collateral or any part thereof, hereby waives all rights, legal
and equitable, it may now or hereafter have to require marshaling of assets or
to require, upon foreclosure, sales of assets in a particular order.  Each
successor and assign of the Grantor, including a holder of a lien subordinate to
the lien created hereby (without implying that the Grantor has, except as
expressly provided herein, a right to grant an interest in, or a subordinate
lien on, any of the Collateral), by acceptance of its interest or lien agrees
that it shall be bound by the above waiver, to the same extent as if such holder
gave the waiver itself.  The Grantor also hereby waives, to the full extent it
may lawfully do so, the benefit of all laws providing for rights of appraisal,
valuation, stay or extension or of redemption after foreclosure now or hereafter
in force.

                                       13
<PAGE>

     Section 5.3    Right of the Administrative Agent to Collect and Service
                    --------------------------------------------------------
Accounts.
---------


     Upon the occurrence and during the continuation of any Event of Default,
and the acceleration of any Loan in accordance with Article VII of the Credit
                                                    -----------
Agreement, the Administrative Agent may notify or may require the Grantor to
notify any person or entity obligated to the Grantor under any account for
monies due or to become due forming all or any part of the Collateral, whether
now existing or hereafter acquired, that the same has been assigned to the
Administrative Agent and that such obligor should make payment or performance of
its obligations under such account directly to the Administrative Agent, and the
Administrative Agent may take possession of and exercise control over all
proceeds of any such account in the Grantor's possession or otherwise, and may
take any other action which the Administrative Agent deems necessary or
desirable to collect any such account or the proceeds thereof.  To evidence the
Administrative Agent's rights hereunder, the Grantor shall, at the Grantor's
expense, execute such assignments or endorsements of any such account, or of the
proceeds thereof, as the Administrative Agent may request.

     Section 5.4    Right of the Administrative Agent to Use, Operate and
                    -----------------------------------------------------
Maintain Collateral.
-------------------

     Section 5.4.1  Rights of the Administrative Agent.
                    ----------------------------------

     Upon the Administrative Agent's taking possession of all or any part of the
Collateral in accordance with the terms of this Security Agreement or otherwise,
the Administrative Agent shall have the right to hold, store, and/or use,
operate, manage, and control the same.  Upon any such taking of possession, the
Administrative Agent may (but shall not be obligated to), from time to time, at
the expense of the Grantor, make all such repairs, replacements, alterations,
additions, and improvements to and of all or any of the Collateral as the
Administrative Agent may deem proper.  In any such case the Administrative Agent
shall have the right to exercise all rights and powers of the Grantor in respect
of the Collateral or any part thereof as the Administrative Agent shall deem
proper, including the right to enter into any and all such agreements with
respect to the leasing and/or operation of the Collateral or any part thereof as
the Administrative Agent may see fit; and the Administrative Agent shall be
entitled to collect and receive all rents, issues, profits, fees, revenues, and
other income of the same and every part thereof.

     Section 5.4.2  The Administrative Agent Has No Duty.
                    ------------------------------------

     The powers conferred on the Administrative Agent hereunder are solely to
protect its interest in the Collateral and shall not impose any duty on it to
exercise any such powers.  Except for the reasonable care and preservation of
any Collateral in its possession and the accounting for moneys actually received
by it hereunder, the Administrative Agent shall have no duty as to any
Collateral or as to the taking of any necessary steps to preserve rights against
prior parties or any other rights pertaining to any Collateral.

                                       14
<PAGE>

     Section 5.5  Right of the Administrative Agent to Appoint Receiver.
                  ------------------------------------------------------

     Upon the occurrence and during the continuation of any Event of Default,
the Administrative Agent shall, as a matter of right and without any requirement
of notice, to the extent permitted under applicable law, be entitled to appoint
a receiver for all or any part of the Collateral, whether such receivership be
incidental to a proposed sale of the Collateral or otherwise.  All disbursements
made by the receiver under this Section 5.5 and the expenses of receivership
                                -----------
shall be added to and be a part of the Obligations, and, whether or not said
principal sum, including such disbursements and expenses, exceeds the
indebtedness originally intended to be secured hereby, the entire amount of said
sum, including such disbursements and expenses, shall be secured by this
Security Agreement and shall be due and payable upon demand therefor and
thereafter shall bear interest at the rate set forth in Section 2.3.E of the
                                                        -------------
Credit Agreement.

     Section 5.6  Remedies Cumulative; Delay Not Waiver.
                  --------------------------------------

     The rights and remedies of the Administrative Agent under the Credit
Agreement, this Security Agreement, the other Loan Documents, or any other
related agreement are cumulative and shall in no way affect, or deprive the
Administrative Agent of, or be deemed to constitute a waiver by the
Administrative Agent of any other rights or remedies allowed to the
Administrative Agent at law or in equity.  No notice to or demand on the Grantor
in any case shall entitle the Grantor to any other notice or demand in similar
or other circumstances and the exercise of any one remedy shall not impair the
Administrative Agent's right simultaneously or at any time or in any order to
exercise any other remedy nor shall the exercise of any remedy in one case
impair or otherwise affect the Administrative Agent's right or ability to
exercise such remedy contemporaneously or again in the same case or in any other
case.  No failure or delay by the Administrative Agent in exercising any right
or power hereunder shall operate as a waiver thereof, nor shall any single or
partial exercise of any such right or power, or any abandonment or
discontinuance of steps to enforce such a right or power, preclude any other or
further exercise thereof or the exercise of any other right or power.

     Section 5.7  Waiver of Rights.
                  -----------------

     To the extent permitted under applicable law, the Grantor waives all rights
and remedies of a debtor or grantor under the UCC or other applicable law, and
all formalities prescribed by law relative to the sale or disposition of the
Collateral (other than notice of sale) after the occurrence and during the
continuation of an Event of Default and all other rights and remedies of the
Grantor with respect thereto.  In exercising its right to take possession of the
Collateral upon the occurrence and during the continuation of an Event of
Default hereunder, the Administrative Agent, personally or by its agents or
attorneys, and subject to the rights of any tenant under any lease or sublease
of the Collateral, to the fullest extent permitted by law, may enter upon any
land owned or leased by the Grantor without being guilty of trespass or any
wrongdoing, and without liability for damages thereby occasioned.  In the event
the Administrative Agent elects to proceed with respect to the Collateral,
separately from any real property, the Administrative

                                       15
<PAGE>

Agent shall give the Grantor at least ten (10) days' notice of the sale of the
Collateral, which shall for all purposes be deemed to be commercially
reasonable.

     Section 5.8  Compliance with Restrictions.
                  -----------------------------

     The Grantor agrees that in any sale of any of the Collateral whenever an
Event of Default shall have occurred and be continuing, the Administrative Agent
is hereby authorized to comply with any limitation or restriction in connection
with such sale as it may be advised by counsel is necessary in order to avoid
any violation of applicable law, or in order to obtain any required approval of
the sale or of the purchaser by any governmental regulatory authority or
official, and the Grantor further agrees that such compliance shall not result
in such sale being considered or deemed not to have been made in a commercially
reasonable manner, nor shall the Administrative Agent be liable or accountable
to the Grantor for any discount allowed by reason of the fact that such
Collateral is sold in compliance with any such limitation or restriction.

     Section 5.9  Distribution of Proceeds.
                  -------------------------

     All cash proceeds received by the Administrative Agent in respect of any
sale of, collection from, or other realization upon all or any part of the
Collateral may, in the discretion of the Administrative Agent, be held by the
Administrative Agent as collateral for, and/or then or at any time thereafter
applied (after payment of any amounts payable to the Administrative Agent
pursuant to Section 6.2) in whole or in part by the Administrative Agent for the
            -----------
ratable benefit of the Secured Parties against, all or any part of the
Obligations in such order as the Administrative Agent shall elect.  The Grantor
shall remain liable for any deficiency.  Any surplus of such cash or cash
proceeds held by the Administrative Agent and remaining after payment in full in
cash of all the Obligations, the termination of all Interest Rate Agreements to
which a Secured Party is a party and the termination of all Commitments shall be
paid over to the Grantor or to whomsoever may be lawfully entitled to receive
such surplus.

                                 ARTICLE VI.
                           MISCELLANEOUS PROVISIONS

     Section 6.1  Additional Actions and Documents.
                  ---------------------------------

     The Grantor agrees that at any time, and from time to time, at the expense
of the Grantor, the Grantor will promptly execute and deliver all further
instruments, and take all further action that the Administrative Agent may
reasonably request, in order to perfect and protect any security interest
granted or purported to be granted hereby or to enable the Administrative Agent
to exercise and enforce its rights and remedies hereunder with respect to any
Collateral.  Nothing in this Section 6.1 shall be construed as limiting the
                             -----------
Obligations of the Borrower under Section 5.11 of the Credit Agreement.
                                  ------------

     Section 6.2  Expenses.
                  ---------

                                       16
<PAGE>

     The Grantor agrees to reimburse and save the Administrative Agent harmless
against liability for the payment of all out-of-pocket expenses arising in
connection with the administration or enforcement of, or the preservation or
exercise of, any rights (including the right to collect and dispose of the
Collateral) under, this Security Agreement, including the reasonable fees and
other charges of outside counsel to the Administrative Agent arising in such
connection, and all such fees and other charges shall be added to the Grantor's
obligations secured hereby.

     Section 6.3  Notices.
                  --------

     Any communications between the parties hereto or notices provided herein to
be given shall be sent in accordance with the provisions of, and to the
addresses set forth in, Section 9.8 of the Credit Agreement, and if to the
                        -----------
Grantor, to the following address:

                          Local Fiber, L.L.C.
                          570 Lexington Avenue
                          3rd Floor
                          New York, New York  10022
                          Attn.: President
                          Telecopy: (212) 421-8920

     Section 6.4  Release and Satisfaction.
                  -------------------------

     Upon the indefeasible payment (whether in cash and/or other consideration
which is satisfactory to the Lenders in their sole discretion) and performance
in full of the Obligations, the termination of all Commitments and the
termination of all Interest Rate Agreements to which any Secured Party is a
party, (i) this Security Agreement and the security interest created hereby
shall terminate, and (ii) upon written request of the Grantor, the
Administrative Agent shall execute and deliver to the Grantor, at the Grantor's
expense and without representation or warranty by or recourse to the
Administrative Agent or the Secured Parties, releases and satisfactions of all
financing statements, mortgages, notices of assignment and other registrations
of security, and the Grantor shall deliver to the Administrative Agent a general
release of all of the Administrative Agent's liabilities and obligations under
all Loan Documents and an acknowledgment that the same have been terminated.

     Section 6.5  Benefit.
                  --------

     This Security Agreement shall be binding upon, and shall inure to the
benefit of, the parties hereto and the Secured Parties and their respective
successors, legal representatives and permitted assigns. The Grantor shall not
assign any of its rights or obligations hereunder without the prior written
consent of the Required Lenders.

     Section 6.6  Amendments and Waivers.
                  -----------------------

                                       17
<PAGE>

     No amendment, modification, termination or waiver of any provision of this
Security Agreement, or consent to any departure by the Administrative Agent
therefrom, shall be effective unless the same shall be in writing and signed by
the Administrative Agent and the Grantor and shall comply with the provisions
set forth in Section 9.6 of the Credit Agreement.  Each amendment, modification,
             -----------
termination or waiver shall be effective only in the specific instance and for
the specific purpose for which it was given.

     Section 6.7  Headings.
                  ---------

     Section and subsection headings contained in this Security Agreement are
inserted for convenience of reference only, shall not be deemed to be a part of
this Security Agreement for any purpose, and shall not in any way define or
affect the meaning, construction or scope of any of the provisions hereof.

     Section 6.8  Applicable Law; Entire Agreement.
                  ---------------------------------

     This Security Agreement shall be governed by, and shall be construed and
enforced in accordance with, the internal laws of the State of New York, without
regard to conflicts of laws principles (other than Sections 5-1401 and 5-1402 of
the General Obligations Law of the State of New York), except to the extent that
the validity or perfection of the security interest hereunder, or exercise of
remedies hereunder, in respect of any particular Collateral are governed by the
laws of a jurisdiction other than the State of New York.  This Security
Agreement and the other Loan Documents constitute the entire understanding among
the parties hereto with respect to the subject matter hereof and supersede any
prior agreements, written or oral, with respect thereto.

     Section 6.9  Severability.
                  -------------

     The invalidity, illegality or unenforceability in any jurisdiction of any
provision in or obligation under this Security Agreement shall not affect or
impair the validity, legality or enforceability of the remaining provisions or
obligations under this Security Agreement or of such provision or obligation in
any other jurisdiction.

     Section 6.10 Consent to Jurisdiction.
                  ------------------------

     The Grantor hereby irrevocably and unconditionally submits, for itself and
its property, to the nonexclusive jurisdiction of the Supreme Court of the State
of New York sitting in New York County and of the United States District Court
of the Southern District of New York, and any appellate court in respect
thereof, in any action or proceeding arising out of or relating to this Security
Agreement, or for recognition or enforcement of any judgment, and hereby
irrevocably and unconditionally agrees that all claims in respect of any such
action or proceeding may be heard and determined in such New York State court
or, to the extent permitted by law, in such federal court.  The Grantor agrees
that a final judgment in any such action or proceeding shall be conclusive and
may be enforced in other jurisdictions by suit on the judgment or in any other
manner provided by law. Nothing in this Section 6.10 shall affect any right that
                                        ------------
the

                                       18
<PAGE>

Administrative Agent or any Secured Party may otherwise have to bring any
action or proceeding relating to this Security Agreement against the Grantor or
any of its properties in the courts of any jurisdiction.  The Grantor hereby
irrevocably and unconditionally waives, to the fullest extent it may legally and
effectively do so, any objection which it may now or hereafter have to the
laying of venue of any suit, action or proceeding arising out of or relating to
this Security Agreement in any court referred to in this Section 6.10. The
                                                         ------------
Grantor irrevocably waives, to the fullest extent permitted by law, the defense
of an inconvenient forum to the maintenance of such action or proceeding in any
such court. The Grantor irrevocably consents to service of process in the manner
provided for notices in Section 6.3. Nothing in this Security Agreement will
                        -----------
affect the right of any party hereto to serve process in any other manner
permitted by law.

     Section 6.11  Construction.
                   -------------

     The Grantor and the Administrative Agent each acknowledges that it has had
the benefit of legal counsel of its own choice and has been afforded an
opportunity to review this Security Agreement with its legal counsel and that
this Security Agreement shall be construed as if jointly drafted by the Grantor
and the Administrative Agent.

     Section 6.12  Counterparts; Effectiveness.
                   ----------------------------

     This Security Agreement and any amendments, waivers, consents, or
supplements may be executed in any number of counterparts and by different
parties hereto in separate counterparts, each of which when so executed and
delivered shall be deemed an original, but all of which counterparts together
shall constitute but one and the same instrument.  This Security Agreement shall
become effective upon the execution of a counterpart hereof by each of the
parties hereto.  Delivery of an executed counterpart of a signature page to this
Security Agreement or to any amendments, waivers, consents or supplements hereof
by telecopier shall be as effective as delivery of a manually executed
counterpart thereof.

     Section 6.13  Waiver of Jury Trial.
                   ---------------------

     THE GRANTOR HEREBY WAIVES, TO THE FULLEST EXTENT PERMITTED BY APPLICABLE
LAW, ANY RIGHT IT MAY HAVE TO A TRIAL BY JURY IN ANY LEGAL PROCEEDING DIRECTLY
OR INDIRECTLY ARISING OUT OF OR RELATING TO THIS SECURITY AGREEMENT OR THE
TRANSACTIONS CONTEMPLATED HEREBY (WHETHER BASED ON CONTRACT, TORT OR ANY OTHER
THEORY).


                  [REMAINDER OF PAGE INTENTIONALLY LEFT BLANK]

                                       19
<PAGE>

     IN WITNESS WHEREOF, each of the parties hereto has caused this Subsidiary
Security Agreement to be duly executed and delivered in its name and on its
behalf, all as of the day and year first above written.

                              LOCAL FIBER, L.L.C., as the Grantor

                              By: /s/ Michael S. Liss
                                 --------------------------------
                                 Name:  Michael S. Liss
                                 Title: President

                              DEUTSCHE BANK AG NEW YORK
                                 BRANCH, as Administrative Agent

                              By: /s/ Jon D. Storck
                                 --------------------------------
                                 Name:  Jon D. Storck
                                 Title: Vice President

                              By: /s/ Alexander Richarz
                                 --------------------------------
                                 Name:  Alexander Richarz
                                 Title: Assistant Vice President

                                      S-1

<PAGE>

                                 SCHEDULE 3.4


                             GOVERNMENTAL CONSENTS
                             ---------------------


None.