<PAGE>

                                                                    Exhibit 10.4

      FIRST AMENDMENT OF LEASE dated as of October 1, 2000 by and between THE
RECTOR, CHURCH-WARDENS AND VESTRYMEN OF TRINITY CHURCH IN THE CITY OF NEW YORK,
as Landlord, having its offices at 74 Trinity Place, New York, NY 10006
("Landlord"), and STARMEDIA NETWORK, INC., as Tenant, having its offices at One
Hudson Square, New York, NY 10013 ("Tenant").

                              W I T N E S S E T H :

      WHEREAS, pursuant to a lease dated as of November 22, 1999 (the "Lease"),
Landlord leased to Tenant, and Tenant leased from Landlord, the seventh, eighth
and ninth floors (the "Premises") in the building known as One Hudson Square,
having an address at 75 Varick Street, New York, NY; and

      WHEREAS, possession of the seventh floor premises (the "Seventh Floor
Premises") was to be delivered to the Tenant in accordance with the provisions
of Article Fifty-Two of the Lease; and

      WHEREAS, the parties desire to amend the Lease so as to eliminate the
Seventh Floor Premises from the Premises and to otherwise amend the Lease on the
terms and conditions set forth herein; and

      WHEREAS, capitalized terms used herein shall have the meaning ascribed to
them in the Lease, except as otherwise set forth herein.

      NOW, THEREFORE, the parties hereto agree as follows:

      1. Article FIFTY-TWO, Exhibits E-1 and E-2, and Paragraphs B, C and D of
Exhibit C of the Lease shall be deleted nunc pro tunc, as if the Seventh Floor
Premises and the parties' respective obligations with respect thereto had never
been part of the Premises. Landlord shall not be obligated to lease any of the
Seventh Floor Premises to the Tenant, and the Tenant shall not be obligated to
lease any portion of the Seventh Floor Premises from the Landlord.

      2. As of October 1, 2000 (the "Effective Date"), the fixed rent payable
pursuant to Article ONE of the Lease shall be amended as follows:

      (i)   During the period commencing on the Effective Date and ending on the
            day immediately preceding the third anniversary of the Rent
            Commencement Date, the fixed rent shall be Three Million Five
            Hundred Sixty Nine Thousand Nine Hundred Two and 00/100 Dollars
            ($3,569,902.00), payable in equal monthly installments of Two
            Hundred Ninety Seven Thousand Four Hundred Ninety One and 81/100
            Dollars ($297,491.81); and

      (ii)  During the period commencing on the third anniversary of the Rent
            Commencement Date and ending on the day immediately preceding the
            sixth anniversary of the Rent


<PAGE>

            Commencement Date, the fixed rent shall be Four Million Two Hundred
            Fifty Five Thousand Three Hundred Sixty Seven and 00/100 Dollars
            ($4,255,367.00), payable in equal monthly installments of Three
            Hundred Fifty Four Thousand Six Hundred Thirteen and 89/100 Dollars
            ($354,613.89); and

      (iii) During the period commencing on the sixth anniversary of the Rent
            Commencement Date and ending on the Expiration Date, the fixed rent
            shall be Four Million Six Hundred Sixty Six Thousand Six Hundred
            Forty Six and 00/100 Dollars ($4,666,646.00), payable in equal
            monthly installments of Three Hundred Eighty Eight Thousand Eight
            Hundred Eighty Seven and 14/100 Dollars ($388,887.14).

      3. Exhibit B is deleted in its entirety, and a revised Exhibit B, a copy
of which is annexed hereto, is substituted in lieu thereof.

      4. In addition to the fixed rent and additional rent payable pursuant to
the Lease (as modified by this First Amendment), effective as of October 1, 2002
and on the first day of each month thereafter during the remainder of the term,
the Tenant shall pay the additional sum of $15,778.17 each month, which sum
shall constitute additional rent under the Lease.

      5. In calculating the ten percent of the rentable square footage of the
Premises which may be used for "desk sharing" arrangements or be sublet by
Tenant pursuant to the provisions of Article SEVENTEEN (q), the seventh floor
shall be deemed to be part of the Premises, so that for purposes of Article
SEVENTEEN (q) only, the total rentable square footage of the Premises shall be
deemed to be 210,072 rentable square feet. In calculating changes in the
rentable square footage of the Premises as a result of the addition to or
recapture of any portion of the Premises following the Effective Date, the total
square footage of the Premises shall be calculated as if the seventh floor
premises (consisting of 72,979 rentable square feet) was part of the Premises.

      6. As of September 30, 2000, the required amount of the security deposit
set forth in Article TWENTY-NINE (a) has been reduced to Five Million and 00/100
Dollars ($5,000,000.00). The Landlord shall reasonably cooperate with the Tenant
in exchanging the Letter of Credit currently being held by the Landlord for an
amended Letter of Credit in the reduced amount, or accepting an amendment
thereto, or as may be otherwise reasonably necessary to accomplish the foregoing
reduction in security. In addition, the schedule of the reductions in the
security deposit shall be revised as follows:

      Anniversary of the
      One Year Rent Date                           Amount of Security Deposit
      ------------------                           --------------------------

        1st anniversary                                    $4,583,334

        2nd anniversary                                    $4,166,668

        3rd anniversary                                    $3,750,002

        4th anniversary                                    $3,333,336

<PAGE>

      7. The reference in the seventeenth line of Article FOURTEEN (a)(v) to
Fifteen Million Dollars is hereby amended to Ten Million Dollars
($10,000,000.00).

      8. The Tenant represents and warrants to the Landlord that all of the
Tenant's negotiations respecting this First Amendment of Lease which were
conducted with or through any person, firm or corporation, other than the
officers of the Landlord, were conducted through Williamson, Pickett, Gross,
Inc. (the "Broker"). The Tenant agrees to pay the commission due to the Broker,
if any, with respect to this First Amendment of Lease. Tenant agrees to
indemnify and hold Landlord harmless from and against demands, liabilities,
losses, causes of action, damages, costs and expenses (including, without
limitation, attorneys' fees and disbursements) suffered or incurred in
connection with any claims for a brokerage commission, finder's fee,
consultation fees or other compensation arising out of any conversation or
negotiation had by the Tenant with any broker or other party in connection with
this First Amendment of Lease.

      9. Except as specifically modified herein, the Lease is hereby ratified
and shall remain in full force and effect.

      IN WITNESS WHEREOF, the parties have signed this First Amendment of Lease
as of the date set forth above.


                            LANDLORD:
                            THE RECTOR, CHURCH-WARDENS AND VESTRYMEN
                            OF TRINITY CHURCH IN THE CITY OF NEW YORK

                            By:    /s/ Daniel Paul Matthews
                                 -----------------------------------------------
                                   Daniel Paul Matthews, Rector

                            By:
                                 -----------------------------------------------
                                   Director of Leasing

                            By:
                                 -----------------------------------------------
                                   Executive Vice President of Real Estate

                            By:
                                 -----------------------------------------------
                                   Chief Financial Officer


                            TENANT:
                            STARMEDIA NETWORK, INC.

                            By:     /s/ Jack C. Chen
                                 -----------------------------------------------
                                   Name:  Jack C. Chen
                                   Title: President


<PAGE>

                                REVISED EXHIBIT B
                                 EXPENSE PAYMENT

<TABLE>
<CAPTION>
------------------------------------------------------------------------------------------------------------------------------------
                                                                             Annual                Operating
       Effective Month                    Year                              Base Rent              Escalation         Escalated Rent
       ---------------                    ----                              ---------              ----------         --------------
<S>                                       <C>                               <C>                    <C>                   <C>
------------------------------------------------------------------------------------------------------------------------------------
            May 1                         2000                              3,569,902                      0             3,569,902
------------------------------------------------------------------------------------------------------------------------------------
            May 1                         2001                              3,569,902                107,097             3,676,999
------------------------------------------------------------------------------------------------------------------------------------
            May 1                         2002                              3,569,902                217,407             3,787,309
------------------------------------------------------------------------------------------------------------------------------------
            May 1                         2003                              4,255,367                331,026             4,586,393
------------------------------------------------------------------------------------------------------------------------------------
            May 1                         2004                              4,255,367                468,618             4,723,985
------------------------------------------------------------------------------------------------------------------------------------
            May 1                         2005                              4,255,367                610,338             4,865,705
------------------------------------------------------------------------------------------------------------------------------------
            May 1                         2006                              4,666,646                756,309             5,422,955
------------------------------------------------------------------------------------------------------------------------------------
            May 1                         2007                              4,666,646                918,997             5,585,643
------------------------------------------------------------------------------------------------------------------------------------
            May 1                         2008                              4,666,646              1,086,567             5,753,213
------------------------------------------------------------------------------------------------------------------------------------
            May 1                         2009                              4,666,646              1,259,163             5,925,809
------------------------------------------------------------------------------------------------------------------------------------
            May 1                         2010                              4,666,646              1,436,937             6,103,583
------------------------------------------------------------------------------------------------------------------------------------
            May 1                         2011                              4,666,646              1,620,045             6,286,691
------------------------------------------------------------------------------------------------------------------------------------
</TABLE>