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                                                                     Exhibit 4.1

                       AMENDMENT NO. 1 TO RIGHTS AGREEMENT

            Amendment No. 1, dated as of May 28, 2001 (the "Amendment"), between
STARMEDIA NETWORK, INC., a Delaware corporation (the "Company"), and AMERICAN
STOCK TRANSFER & TRUST COMPANY, a New York banking corporation, as Rights Agent
(the "Rights Agent").

            WHEREAS, the Company and the Rights Agent entered into a Rights
Agreement, dated as of May 21, 1999 (the "Rights Agreement");

            WHEREAS, there is not as of the date hereof any Acquiring Person (as
defined in the Rights Agreement); and

            WHEREAS, the Company desires to amend the Rights Agreement in
accordance with Section 27 of the Rights Agreement;

            NOW, THEREFORE, in consideration of the premises and mutual
agreements set forth in the Rights Agreement and this Amendment, the parties
hereby agree as follows:

            Section 1. AMENDMENT TO DEFINITION OF "ACQUIRING PERSON". The
definition of "Acquiring Person" in Section 1 of the Rights Agreement is hereby
amended to read in its entirety as follows:

            "Acquiring Person" shall mean any Person (as such term is
      hereinafter defined) who or which, together with all Affiliates and
      Associates (as such terms are hereinafter defined) of such Person, shall
      be the Beneficial Owner (as such term is hereinafter defined) of 15% or
      more of the shares of Common Stock of the Company then outstanding but
      shall not include (1) the Company, any Subsidiary (as such term is
      hereinafter defined) of the Company, any employee benefit plan of the
      Company or any Subsidiary of the Company, or any entity holding shares of
      Common Stock for or pursuant to the terms of any such plan, (2) Chase
      Venture Capital Associates, L.P. ("Chase") or any Affiliates or Associates
      of Chase (the "Chase Group") to the extent that the members of the Chase
      Group shall beneficially own in the aggregate up to, but not exceeding,
      25% of the shares of Common Stock of the Company then outstanding, (3)
      Fernando J. Espuelas or any Affiliates or Associates of Mr. Espuelas (the
      "Espuelas Group") to the extent that the members of the Espuelas Group
      shall beneficially own in the aggregate up to, but not exceeding, 20% of
      the shares of Common Stock of the Company then outstanding, (4) Jack C.
      Chen or any Affiliates or Associates of Mr. Chen (the "Chen Group") to the
      extent that the members of the Chen Group shall beneficially own in the
      aggregate up to, but not exceeding, 20% of the shares of Common Stock of
      the Company then outstanding, or (5) BellSouth Enterprises, Inc.
      ("BellSouth") or any Affiliates or Associates of BellSouth (the "BellSouth
      Group") to the extent that the members of the BellSouth Group shall
      beneficially

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      own in the aggregate up to, but not exceeding 25% of the shares of Common
      Stock of the Company then outstanding. Notwithstanding the foregoing:

                  (i) no Person shall become an "Acquiring Person" as the result
            of an acquisition of shares of Common Stock by the Company which, by
            reducing the number of shares outstanding, increases the
            proportionate number of shares beneficially owned by such Person to
            15% or more of the shares of Common Stock of the Company then
            outstanding (or, in the case of (A) the Chase Group, more than 25%
            of the shares of Common Stock of the Company then outstanding, (B)
            either the Espuelas Group or the Chen Group, more than 20% of the
            shares of Common Stock of the Company then outstanding, or (C) the
            BellSouth Group, more than 25% of the shares of Common Stock of the
            Company then outstanding); PROVIDED, HOWEVER, that if a Person shall
            become the Beneficial Owner of 15% or more of the shares of Common
            Stock of the Company then outstanding (or, in the case of (D) the
            Chase Group, more than 25% of the shares of Common Stock of the
            Company then outstanding, (E) either the Espuelas Group or the Chen
            Group, more than 20% of the shares of Common Stock of the Company
            then outstanding, or (F) the BellSouth Group, more than 25% of the
            shares of Common Stock of the Company then outstanding) by reason of
            share purchases by the Company and shall, after such share purchases
            by the Company, become the Beneficial Owner of any additional shares
            of Common Stock of the Company (or, in the case of the members of
            any of the Chase Group, the Espuelas Group, the Chen Group or the
            BellSouth Group, become the Beneficial Owner of any additional
            shares of Common Stock of the Company), then such Person shall be
            deemed to be an "Acquiring Person" hereunder; and

                  (ii) if the Board of Directors of the Company determines in
            good faith that a Person who would otherwise be an "Acquiring
            Person" as defined pursuant to the foregoing provisions of this
            paragraph (a), has become such inadvertently, and such Person
            divests as promptly as practicable a sufficient number of shares of
            Common Stock so that such Person would no longer be an "Acquiring
            Person" (as defined pursuant to the foregoing provisions of this
            paragraph (a)), then such Person shall not be deemed to be an
            "Acquiring Person" for any purpose of this Agreement.

            Section 2. AMENDMENT TO DEFINITIONS OF "BENEFICIAL OWNER" AND
"BENEFICIALLY OWN". The definitions of "Beneficial Owner" and "beneficially own"
in Section 1 of the Rights Agreement are hereby amended by adding at the end
thereof:

            "Notwithstanding anything in this definition of "Beneficial
      Ownership" and "beneficially own" to the contrary, no member of the
      BellSouth Group shall be deemed the "Beneficial Owner" of, or to
      "beneficially own", any security owned by Fernando J. Espuelas or Jack C.
      Chen solely by reason of that certain

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      Voting Agreement, dated as of May 30, 2001, by and among BellSouth,
      Fernando J. Espuelas and Jack C. Chen."

            Section 3. RIGHTS AGREEMENT AS AMENDED. The term "Agreement" as used
in the Rights Agreement shall be deemed to refer to the Rights Agreement as
amended hereby. The foregoing amendments shall be effective as of the date
hereof and, except as set forth herein, the Rights Agreement shall remain in
full force and effect and shall be otherwise unaffected hereby.

            Section 4. COUNTERPARTS. This Amendment may be executed in any
number of counterparts, and each of such counterparts shall for all purposes be
deemed an original, but all such counterparts shall together constitute but one
and the same instrument.

            Section 5. GOVERNING LAW. This Amendment shall be deemed to be a
contract made under the laws of the State of New York and for all purposes shall
be governed by and construed in accordance with the laws of such State
applicable to contracts made and to be performed entirely within such State.

            Section 6. HEADINGS. Headings of the several Sections of the
Amendment are inserted for convenience only and shall not control or affect the
meaning or construction of any of the provisions hereof.

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            IN WITNESS WHEREOF, the parties hereto have caused this Amendment to
be duly executed as of the day and year first above written.


                                 STARMEDIA NETWORKS, INC.


                                 By: /s/ Justin K. Macedonia
                                     -------------------------------------------
                                     Name:  Justin K. Macedonia
                                     Title: Senior Vice President and General
                                            Counsel


                                 AMERICAN STOCK TRANSFER &
                                 TRUST COMPANY, as Rights Agent


                                 By: /s/ Herbert J. Lemmer
                                     -------------------------------------------
                                     Name:  Herbert J. Lemmer
                                     Title: Vice President