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                                                                     Exhibit 4.1

                 AMENDMENT NO. 1 TO STOCKHOLDER RIGHTS AGREEMENT

      AMENDMENT NO. 1, dated as of January 23, 2004 (this "Amendment"), to the
Stockholder Rights Agreement dated as of March 7, 2003 (the "Rights Agreement")
by and between FreeMarkets, Inc., a Delaware corporation (the "Corporation"),
and American Stock Transfer & Trust Company, a New York corporation (the "Rights
Agent"). Capitalized terms used in this Amendment but not defined herein shall
have the meaning given to such terms in the Rights Agreement.

      WHEREAS, the Corporation intends to enter into an Agreement and Plan of
Merger and Reorganization (the "Merger Agreement") with Ariba, Inc., a Delaware
corporation ("Ariba"), and Fleet Merger Corporation, a Delaware corporation
("Merger Sub"), pursuant to which (i) Merger Sub will merge with and into the
Company (the "Reverse Merger") and (ii) the Company will merge with and into
Ariba (the "Second-Step Merger"), both steps of which will occur as part of a
single integrated plan (collectively, the "Merger").

      WHEREAS, concurrently with the execution of the Merger Agreement, certain
stockholders of the Corporation are entering into voting agreements with Ariba
(the "Voting Agreements").

      WHEREAS, pursuant to Section 27 of the Rights Agreement, the Corporation
may amend the Rights Agreement in any respect without the approval of any
holders of Rights and the Rights Agent shall, if the Corporation so directs,
execute such supplement or amendment.

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

      Section 1. Amendments to Rights Agreement. The Rights Agreement is hereby
amended as follows:

            (a) The definition of "Acquiring Person" in Section 1(a) of the
Rights Agreement is amended to add the following subparagraph (iii) at the end
thereof:

            "(iii) Notwithstanding any provision in this Rights Agreement to the
            contrary, no Person (including Parent (as defined in the Merger
            Agreement) or any of its Affiliates or Associates) shall be or
            become an Acquiring Person solely by reason of (i) the adoption,
            approval, execution or delivery of the Merger Agreement and the
            Voting Agreements, (ii) the public announcement of such adoption,
            approval, execution or delivery or (iii) the consummation of the
            Merger or any of the other transactions contemplated or permitted by
            the Merger Agreement."
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            (b) The definition of "Distribution Date" in Section 1(j) of the
Rights Agreement is amended to add the following sentence at the end thereof.

            "Notwithstanding any provision in this Rights Agreement to the
            contrary, a Distribution Date shall not be deemed to have occurred
            solely by reason of the (i) adoption, approval, execution or
            delivery of the Merger Agreement and the Voting Agreements, (ii) the
            public announcement of such adoption, approval, execution or
            delivery or (iii) the consummation of the Merger or any of the other
            transactions contemplated or permitted by the Merger Agreement."

            (c) The definition of "Stock Acquisition Date" in Section 1(aa) of
the Rights Agreement is amended to add the following sentence at the end
thereof.

            "Notwithstanding any provision in this Rights Agreement to the
            contrary, a Stock Acquisition Date shall not be deemed to have
            occurred solely by reason of the (i) adoption, approval, execution
            or delivery of the Merger Agreement and the Voting Agreements, (ii)
            the public announcement of such adoption, approval, execution or
            delivery or (iii) the consummation of the Merger or any of the other
            transactions contemplated or permitted by the Merger Agreement."

            (d) Amendment of Section 7. Section 7(a) of the Rights Agreement is
amended and restated in its entirety as follows:

            "(a) Prior to the earlier of (i) the Close of Business on March 7,
            2013 (the "Final Expiration Date"), (ii) the time at which the
            Rights are redeemed as provided in Section 23 hereof, (iii) the time
            at which the Rights are exchanged as provided in Section 24 hereof
            or (iv) the time immediately prior to the Effective Time (as defined
            in the Merger Agreement) (the earlier of (i), (ii), (iii) and (iv)
            being the "Expiration Date"), the registered holder of any Rights
            Certificate may, subject to the provisions of Sections 7(e) and 9(c)
            hereof, exercise the Rights evidenced thereby (except as otherwise
            provided herein) in whole or in part at any time after the
            Distribution Date upon surrender of the Rights Certificate, with the
            form of election to purchase and the certificate on the reverse side
            thereof duly executed, to the Rights Agent at the office of the
            Rights Agent designated for such purpose, together with payment of
            the aggregate Purchase Price (as hereinafter defined) for the number
            of Units of Series A Preferred Stock (or, following a Triggering
            Event, other securities, cash or other assets, as the case may be)
            for which such surrendered Rights are then exercisable."

            (e) Amendment of Section 11(a)(ii). Section 11(a)(ii) of the Rights
Agreement is amended to add the following sentence at the end thereof.


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            "A Section 11(a)(ii) Event shall not be deemed to have occurred
            solely by reason of the (i) adoption, approval, execution or
            delivery of the Merger Agreement and the Voting Agreements, (ii) the
            public announcement of such adoption, approval, execution or
            delivery or (iii) the consummation of the Merger or any of the other
            transactions contemplated or permitted by the Merger Agreement."

            (f) Amendment of Section 13(a). Section 13(a) of the Rights
Agreement is amended to add the following sentence at the end thereof.

            "A Section 13(a) Event shall not be deemed to have occurred solely
            by reason of the (i) adoption, approval, execution or delivery of
            the Merger Agreement and the Voting Agreements, (ii) the public
            announcement of such adoption, approval, execution or delivery or
            (iii) the consummation of the Merger or any of the other
            transactions contemplated or permitted by the Merger Agreement."

            (g) The Rights Agreement is hereby further amended by adding a new
Section 35 immediately after the end of Section 34 thereof to read in its
entirety as follows:

            "Section 35. Merger Agreement with Ariba. Notwithstanding any
            provision in this Rights Agreement to the contrary, none of (i) the
            adoption, approval, execution or delivery of the Merger Agreement
            and the Voting Agreements, (ii) the public announcement of such
            adoption, approval, execution or delivery or (iii) the consummation
            of the Merger or any of the other transactions contemplated or
            permitted by the Merger Agreement is or shall be deemed to be an
            event described in Section 11(a)(ii) or Section 13 hereof, nor will
            such adoption, approval, execution, delivery, announcement or
            consummation result in the occurrence of a Stock Acquisition Date, a
            Distribution Date, a Triggering Event or any other event that causes
            a separation of the Rights from the underlying Common Stock, entitle
            or permit the holders of the Rights to exercise the Rights or
            otherwise affect the rights of the holders of Rights, including by
            giving the holders of the Rights the right to acquire securities of
            any party to the Merger Agreement.

      Section 2. Effectiveness. When executed by the Company, this Amendment
shall be deemed effective as of the date first-written above as if executed on
such date. Except as amended hereby, the Rights Agreement shall remain in full
force and effect and shall otherwise be unaffected hereby.


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      Section 3. Governing Law. 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.

      Section 4. Counterparts. This Agreement may be executed in one or more
counterparts, and by the different parties hereto in separate counterparts, each
of which when executed shall be deemed to be an original, but all of which taken
together shall constitute one and the same instrument.

      Section 5. Descriptive Headings. The headings contained in this Amendment
are for descriptive purposes only and shall not affect in any way the meaning or
interpretation of this Agreement.

      Section 6. Rights Agreement as Amended. Upon the effectiveness of this
Amendment, the term "Rights Agreement" as used in the Rights Agreement shall
refer to the Rights Agreement as amended hereby.


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

                                    FREEMARKETS, INC.


                                    By:  /s/ David H. McCormick
                                        --------------------------------
                                         David H. McCormick
                                         Chief Executive Officer



                                    AMERICAN STOCK TRANSFER &
                                    TRUST COMPANY, as Rights Agent

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


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