EXHIBIT 4.1

                           AMENDMENT TO RIGHTS AGREEMENT

          THIS AMENDMENT (the "Amendment"), is entered into as of June 2, 1999,
by and between TRIANGLE PHARMACEUTICALS, INC., a Delaware corporation (the
"Company"), and AMERICAN STOCK TRANSFER & TRUST COMPANY, as Rights Agent (the
"Rights Agent").

                                      RECITALS

          A.   The Company and the Rights Agent are parties to a Rights
Agreement dated as of February 1, 1999 (the "Rights Agreement").

          B.   Abbott Laboratories, an Illinois corporation ("Abbott"), and the
Company have entered into a Collaboration Agreement made as of June 2, 1999 (the
"Collaboration Agreement"), pursuant to which the parties shall collaborate with
respect to the clinical development, registration, distribution and marketing of
various drugs.

          C.   In connection with the Collaboration Agreement, Abbott and the
Company have entered into, among other agreements, (i) a Common Stock Purchase
Agreement, made as of June 2, 1999 (the "Abbott Stock Purchase Agreement"),
pursuant to which Abbott is to purchase the Shares (as such term is defined in
Section 1.4 of the Abbott Stock Purchase Agreement) and (ii) a Stockholder
Rights Agreement made as of June 2, 1999 (the "Abbott Rights Agreement").

          D.   Pursuant to Section 3.9 of the Abbott Stock Purchase Agreement
and Section 7.1 of the Abbott Rights Agreement, the Board of Directors of the
Company has determined that an amendment to the Rights Agreement as set forth
herein is necessary and desirable to reflect the foregoing and certain other
matters and the Company and the Rights Agent desire to evidence such amendment
in writing.

          Accordingly, the parties agree that:

     1.   AMENDMENT TO DEFINITION OF "ACQUIRING PERSON" SET FORTH IN SECTION
1(a).  The definition of "Acquiring Person" set forth in Section 1(a) of the
Rights Agreement is amended to read in its entirety as follows:

     (a)  "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) during the Interim Period (as defined
     below), Abbott Laboratories, an Illinois corporation (the "Permitted
     Investor"), or any U.S. wholly-owned subsidiaries of Abbott (collectively
     with the Permitted Investor, the



     "Investor Group") but only to the extent that the Permitted Investor may be
     deemed a Beneficial Owner of the Shares (as defined below) as a result of
     the Permitted Investor entering into the Abbott Stock Purchase Agreement
     (as defined below), unless the Permitted Investor becomes the Beneficial
     Owner (as defined in the Abbott Rights Agreement (as defined below)) of any
     additional securities of the Company other than the Shares during the
     Interim Period, or (3) during the Threshold Period (as hereinafter
     defined), the Investor Group.  For purposes of this Agreement, the "Interim
     Period" shall mean such period commencing as of the date of the Abbott
     Stock Purchase Agreement and ending on the earlier of (x) the "Effective
     Date" as such term is defined in the Collaboration Agreement (as defined
     below) and (y) termination of the Abbott Stock Purchase Agreement.  For
     purposes of this Agreement, the "Threshold Period" shall mean such period
     commencing as of the Effective Date under the Collaboration Agreement and
     ending on the earlier of (xx) such time as the Permitted Investor holds
     less than the Minimum Purchaser Interest in the Company (as defined in
     Section 1.11 of the Abbott Rights Agreement), (yy) such time as the
     Investor Group's Beneficial Ownership (as the term Beneficial Ownership is
     defined in the Abbott Rights Agreement) exceeds the Beneficial Ownership
     Limitation (as defined in Section 5.2(a) of the Abbott Rights Agreement),
     and (zz) such time as the Permitted Investor's rights under Section 7.1 of
     the Abbott Rights Agreement have terminated pursuant to the terms of the
     Abbott Rights Agreement.  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, (a) 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, (b) in the case
     of the Investor Group during the Interim Period, increases the
     proportionate number of shares which may be deemed beneficially owned by
     the Investor Group, unless the Permitted Investor becomes the Beneficial
     Owner (as defined in the Abbott Rights Agreement) of any additional
     securities of the Company other than the Shares during the Interim Period,
     or, (c) in the case of the Investor Group during the Threshold Period,
     increases the proportionate number of shares Beneficially Owned (as defined
     in the Abbott Rights Agreement) by the Investor Group to more than the
     Beneficial Ownership Limitation; provided, however, that if by reason of
     share purchases by the Company, (1) a Person shall become the Beneficial
     Owner of 15% or more of the shares of Common Stock of the Company then
     outstanding or, (2) in the case of the Investor Group, the Investor Group's
     ownership increases the Investor Group's Beneficial Ownership (as defined
     in the Abbott Rights Agreement) by any amount during the Interim Period or
     results in the Investor Group's Beneficial Ownership (as defined in the
     Abbott Rights Agreement) to exceed the Beneficial Ownership Limitation at
     any time during the Threshold Period, and, in the case of (1) or (2) above,
     such Person or Investor Group shall, after such share purchases by the
     Company, become the Beneficial Owner of any additional shares of Common
     Stock of the Company, then such Person, including the Investor Group, 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


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     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."

     2.   AMENDMENT TO DEFINITION OF "TRIGGERING EVENT" SET FORTH IN SECTION
1(oo).  The definition of "Triggering Event" set forth in Section 1 (oo) of the
Rights Agreement is amended to add the following sentence to the end thereof:

     "Notwithstanding anything in this Rights Agreement to the contrary, a
     Triggering Event shall not be deemed to have occurred by virtue of the
     Abbott Stock Purchase Agreement and the Related Agreements (as such term is
     defined in the Abbott Stock Purchase Agreement) or by virtue of any of the
     transactions contemplated thereby (excluding during the Interim Period, any
     purchases which result in the Permitted Investor becoming the Beneficial
     Owner (as defined in the Abbott Rights Agreement) of any securities of the
     Company in addition to the Shares and excluding, during the Threshold
     Period, any purchases permitted by Section 5.3 of the Abbott Rights
     Agreement or otherwise which cause the Permitted Investor's Beneficial
     Ownership (as defined in Section 5.4 of the Abbott Rights Agreement) of
     shares of Common Stock to exceed 21% of the then total outstanding shares
     of Common Stock of the Company)."

     3.   AMENDMENT TO SECTION 1.  The following definitions are hereby added to
the end of Section 1 as Sections 1(pp), 1(qq), 1(rr) and 1(ss):

     "(pp)     "Abbott Rights Agreement" shall mean that certain Stockholder
     Rights Agreement made as of June 2, 1999, by and between the Company and
     Abbott Laboratories.

     (qq)  "Abbott Stock Purchase Agreement" shall mean that certain Common
     Stock Purchase Agreement made as of June 2, 1999, by and between the
     Company and Abbott Laboratories.

     (rr) "Collaboration Agreement" shall mean that certain Collaboration
     Agreement made as of June 2, 1999, by and between the Company and Abbott
     Laboratories.

     (ss) "Shares" shall have the meaning assigned to such term in the Abbott
     Stock Purchase Agreement."

     4.   AMENDMENT OF SECTION 3(A).  The first sentence of Section 3(a) of the
Rights Agreement is amended to read in its entirety as follows:

     "Until the earlier of (i) the Close of Business on the Shares
     Acquisition Date and (ii) the Close of Business on the tenth Business
     Day (or such later date as may be determined by action of the
     Company's Board of Directors prior to such time as any Person becomes
     an Acquiring Person and of which the Company will give the Rights
     Agent prompt written notice) after the date that a tender or exchange
     offer


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     by any Person (other than the Company, any Subsidiary of the Company, any
     employee benefit plan of the Company or of any Subsidiary of the Company or
     any entity holding shares of Common Stock for or pursuant to the terms of
     any such plan) is first published or sent or given within the meaning of
     Rule 14d-4(a) of the Exchange Act Regulations or any successor rule or of
     the first public announcement of the intention of any Person (other than
     the Company, any Subsidiary of the Company, any employee benefit plan of
     the Company or of any Subsidiary of the Company or any entity holding
     shares of Common Stock for or pursuant to the terms of any such plan) to
     commence, a tender or exchange offer, if upon consummation thereof such
     Person would be the Beneficial Owner of 15% or more of the shares of
     Company Common Stock then outstanding, or, in the case of the Investor
     Group during the Interim Period, the Investor Group purchases any
     securities of the Company which result in the Permitted Investor becoming
     the Beneficial Owner (as defined in the Abbott Rights Agreement) of any
     securities of the Company in addition to the Shares, or in the case of the
     Investor Group during the Threshold Period, the Permitted Investor's
     Beneficial Ownership (as defined in the Abbott Rights Agreement) would
     exceed the Beneficial Ownership Limitation (as defined in the Abbott Rights
     Agreement), (the earlier of (i) and (ii) above being the "Distribution
     Date"), (x) the Rights will be evidenced (subject to the provisions of
     Section 3(b) hereof) by the certificates for shares of Common Stock
     registered in the names of the holders thereof (which certificates shall
     also be deemed to be Rights Certificates) and not by separate Rights
     Certificates, and (y) the right to receive Rights Certificates will be
     transferable only in connection with the transfer of shares of Common
     Stock."

     5.   MISCELLANEOUS.  This Amendment shall be deemed to be a contract
made under the laws of the State of Delaware and for all purposes shall be
governed by and construed in accordance with the laws of such State
applicable to contracts to be made and performed entirely within such State.
This Amendment may be executed in any number of counterparts, each of such
counterparts shall for all purposes be deemed to be an original, and all such
counterparts shall together constitute but one and the same instrument.  If
any term, provision, covenant or restriction of this Amendment is held by a
court of competent jurisdiction or other authority to be invalid, void or
unenforceable, the remainder of the terms, provisions, covenants and
restrictions of this Amendment shall remain in full force and effect and
shall in no way be affected, impaired or invalidated.

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


 ATTEST:                                 TRIANGLE PHARMACEUTICALS, INC.


 By:  /s/ Chris A. Rallis                By:  /s/ David Barry
    ------------------------------           -------------------------------
      Name:     Chris A. Rallis               Name:   David Barry
            ----------------------                  ------------------------
      Title:    General Counsel               Title:  Chief Executive Officer
            ----------------------                  -------------------------

 ATTEST:                                 AMERICAN STOCK TRANSFER & TRUST
                                         COMPANY


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


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