FIRST AMENDMENT TO RIGHTS AGREEMENT

Exhibit 4.2

FIRST AMENDMENT TO RIGHTS AGREEMENT

This FIRST AMENDMENT TO RIGHTS AGREEMENT, dated as of April 27, 2004 (this “Amendment”), is entered into by and between i2 Technologies, Inc., a Delaware corporation (the “Company”), and Mellon Investor Services LLC, a New Jersey limited liability company (the “Rights Agent”).

RECITALS:

WHEREAS, the Company and the Rights Agent entered into a Rights Agreement, dated as of January 17, 2002 (the “Rights Agreement”);

WHEREAS, Section 27 of the Rights Agreement provides that, in certain circumstances, the Company may from time to time supplement or amend the Rights Agreement, without the approval of any holders of Rights, by action of the Company’s board of directors;

WHEREAS, the Company intends to enter into a Preferred Stock Purchase Agreement (the “Preferred Stock Purchase Agreement”) by and between the Company and R² Investments, LDC, a Cayman Islands limited duration company (the “Investor”), pursuant to which the Company will issue and sell, and the Investor will purchase, 100,000 shares (the “Shares”) of the Company’s 2.5% Series B Convertible Preferred Stock, par value $0.001 per share (the “Series B Preferred Stock”);

WHEREAS, on April 27, 2004, the Special Committee of the Board of Directors of the Company resolved to amend the Rights Agreement to ensure that the Investor (or any Affiliate or Associate thereof) is not intended to be nor will be deemed to be an “Acquiring Person” nor, under any circumstances, will a “Share Acquisition Date” nor a “Distribution Date” be triggered within the meaning of the Rights Agreement, after taking into account the shares of Common Stock beneficially owned as of the date of the Preferred Stock Purchase Agreement and shares of Common Stock that may be issued upon conversion of any securities convertible into or exchangeable for Common Stock (“Common Stock Equivalents”) beneficially owned as of the date of the Preferred Stock Purchase Agreement by the Investor (or any Affiliate or Associate thereof) (the “Current Ownership Interest”), as a result of (i) the execution and delivery of the Preferred Stock Purchase Agreement and the consummation of the transactions contemplated thereby, including but not limited to the acquisition of the Shares or shares of Common Stock upon a conversion in accordance with the Certificate of Designations of the Series B Preferred Stock (the “Certificate of Designations”), (ii) the acquisition of the Shares, the shares of Common Stock upon a conversion in accordance with the Certificate of Designations and the acquisition of any additional securities pursuant to the terms of the Preferred Stock Purchase Agreement or (iii) the acquisition of shares of Common Stock (whether directly or indirectly through the acquisition of Common Stock Equivalents) after the date of the Preferred Stock Purchase Agreement other than Shares or shares of Common Stock described in (i) or (ii); provided that such amount specified in this clause

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(iii) when added to the Current Ownership Interest does not exceed 15% of the shares of Common Stock then outstanding; and

WHEREAS, the Company desires to modify the terms of the Rights Agreement in certain respects as set forth herein, and in connection therewith, is entering into this Amendment and directing the Rights Agent to enter into this Amendment;

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

1. Effect of Amendment. Except as expressly provided herein, the Rights Agreement shall be and remain in full force and effect.

2. Capitalized Terms. All capitalized, undefined terms used in this Amendment shall have the meanings assigned thereto in the Rights Agreement.

3. Amendments to Section 1.

(a) 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 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 of the Company for or pursuant to the terms of any such plan. 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; 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 as a result of any such acquisition of shares of Common Stock by the Company and shall, after such acquisition of shares by the Company, become the Beneficial Owner of any additional shares of Common Stock of the Company (other than as a result of a stock dividend, stock split or similar transaction effected by the Company in which all holders of Common Stock of the Company are treated equally), then such Person shall be deemed to be an ‘Acquiring Person;’

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(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 provisions of subparagraph (i), has become such inadvertently, and such Person divests as promptly as practicable a sufficient number of shares of Common Stock of the Company so that such Person would no longer be an ‘Acquiring Person,’ then such Person shall not be deemed to be an ‘Acquiring Person’ for any purpose of this Agreement;

(iii) Sanjiv S. Sidhu, together with his spouse, lineal descendants (whether by blood or adoption) and any Persons (whether now or hereafter existing) formed primarily for Mr. Sidhu’s or his spouse’s or his lineal descendants’ estate planning purposes, shall not be deemed an Acquiring Person with respect to (x) shares beneficially owned as of the date of this Agreement or (y) additional shares as to which Mr. Sidhu, his spouse, any such lineal descendants or any other such Person acquires Beneficial Ownership after the date of this Agreement, provided that if the aggregate amount of additional shares of Common Stock of the Company acquired pursuant to clause (y) exceeds 5% of the shares of Common Stock outstanding at the first such acquisition described in clause (y) of additional shares of Common Stock of the Company (as such amount may be appropriately adjusted for such events as stock splits, stock dividends and recapitalizations with respect to shares of Common Stock of the Company), then all shares described in (x) and (y) shall be included for purposes of determining whether or not Mr. Sidhu, his spouse, any such lineal descendants or any other such Person is an Acquiring Person; and

(iv) Neither the Investor (as such term is hereinafter defined) nor any of its Affiliates or Associates shall be deemed Acquiring Persons on account of (w) shares beneficially owned as of the date of the Preferred Stock Purchase Agreement (as such term is hereinafter defined) and shares of Common Stock issuable upon conversion of the Common Stock Equivalents (as such term is hereinafter defined) beneficially owned as of the date of the Preferred Stock Purchase Agreement, (x) the execution and delivery of the Preferred Stock Purchase Agreement and the consummation of the transactions contemplated thereby, including but not limited to (1) the acquisition of the Shares (as such term is hereinafter defined) or shares of Common Stock upon a conversion in accordance with the Certificate of Designations (as such term is hereinafter defined), and (2) the acquisition of any additional securities pursuant to the terms of the Preferred Stock Purchase Agreement, (y) the acquisition of shares of Common Stock or Common Stock Equivalents after the date of the Preferred Stock Purchase Agreement other than Shares or shares of Common Stock described in (x) (provided that such amount specified in this clause (y) when added to the amount specified in clause (w) does not

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exceed 15% of the shares of Common Stock then outstanding) and (z) any additional shares of Common Stock or Common Stock Equivalents acquired pursuant to a dividend, distribution or antidilution adjustment paid or made by the Company on the outstanding Common Stock, Common Stock Equivalents or the Series B Preferred Stock (as such term is hereinafter defined) or pursuant to a split or subdivision of the outstanding Common Stock, Common Stock Equivalents or the Series B Preferred Stock.”

(b) The definitions contained in Section 1 of the Rights Agreement shall be supplemented by adding the following definitions in correct alphabetical order:

“Certificate of Designations” shall mean the Certificate of Designations of Series B Preferred Stock.

“Common Stock Equivalent” shall mean any security convertible into or exchangeable for Common Stock.

“Investor” shall mean R² Investments, LDC, a Cayman Islands limited duration company.

“Preferred Stock Purchase Agreement” shall mean the Preferred Stock Purchase Agreement to be entered into by and between the Company and the Investor.

“Series B Preferred Stock” or “Shares” shall mean the number of shares of the Company’s Series B Convertible Preferred Stock, par value $0.001 per share, to be issued and sold to the Investor pursuant to the Preferred Stock Purchase Agreement, plus any and all shares of the Company’s Series B Convertible Preferred Stock, par value $0.001 per share, paid to the Investor as a dividend on such shares or portion thereof.

4. New Section 35. Section 35 is hereby added to the Rights Agreement to read in its entirety as follows:

“Section 35. The Preferred Stock Purchase Agreement. Notwithstanding anything contained in this Agreement to the contrary, neither the approval, execution or delivery of the Preferred Stock Purchase Agreement nor the consummation of the transactions contemplated thereby or the performance of the Company’s obligations thereunder or under the Certificate of Designations shall cause (i) the Investor or any of its Affiliates or Associates to be an Acquiring Person, (ii) a Share Acquisition Date to occur or (iii) a Distribution Date to occur.”

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5. Effective Date. This Amendment is effective as of April 27, 2004, immediately prior to the execution and delivery of the Preferred Stock Purchase Agreement.

6. Governing Law. This Amendment shall be governed by, construed and enforced in accordance with the laws of the State of Delaware without reference to the conflicts or choice of law principles thereof; provided, however, that all provisions regarding the rights, duties and obligations of the Rights Agent shall be governed by and construed in accordance with the laws of the State of New York applicable to contracts made and to be performed entirely within such State.

7. Counterparts; Facsimile Signatures. This Amendment may be executed in any number of counterparts (including facsimile signature) each of which shall be an original with the same effect as if the signatures thereto and hereto were upon the same instrument.

8. Headings. The headings in this Amendment are included for convenience of reference only and shall be ignored in the construction or interpretation hereof.

[Remainder of Page Intentionally Left Blank; Signature Page Follows]

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