as Issuer and THE BANK OF NEW YORK MELLON TRUSTCOMPANY, N.A. as Trustee FIRST SUPPLEMENTAL INDENTURE Dated as of September 11, 2008 To 5% SENIOR CONVERTIBLE NOTES DUE 2015

Exhibit 4.1

Execution Copy

i2 TECHNOLOGIES, INC.

as Issuer

and

THE BANK OF NEW YORK MELLON TRUST COMPANY, N.A.

as Trustee

FIRST SUPPLEMENTAL INDENTURE

Dated as of September 11, 2008

To

5% SENIOR CONVERTIBLE NOTES DUE 2015

INDENTURE

Dated as of November 23, 2005

TABLE OF CONTENTS

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FIRST SUPPLEMENTAL INDENTURE, dated as of September 11, 2008 (this “First Supplemental Indenture”), between i2 TECHNOLOGIES, INC., a Delaware corporation (the “Company”), and THE BANK OF NEW YORK MELLON TRUST COMPANY, N.A., a national banking association (successor-in-interest to JPMorgan Chase Bank, National Association), as trustee under the Indenture referred to below (in such capacity, the “Trustee”).

RECITALS OF THE COMPANY

WHEREAS, the Company and the Trustee are parties to an Indenture, dated as of November 23, 2005 (the “Indenture”) and the Company has issued pursuant to the Indenture the Company’s 5% Senior Convertible Notes due 2015 (the “Securities”); and

WHEREAS, Section 11.2 of the Indenture provides that, among other things, with the written consent of the Holders of at least a majority in aggregate principal amount of the Securities then outstanding, the Company and the Trustee may amend or supplement the Indenture in accordance with the terms and conditions provided therein;

WHEREAS, the Company has entered into an Agreement and Plan of Merger dated August 10, 2008 (the “Merger Agreement”) with JDA Software Group, Inc., a Delaware corporation (“Parent”), and Iceberg Acquisition Corp., a Delaware corporation and a wholly-owned Subsidiary of Parent (“Merger Sub”) pursuant to which Merger Sub will merge with and into the Company, with the Company surviving as a wholly-owned subsidiary of Parent (“Merger”);

WHEREAS, it is a condition precedent to the consummation of the Merger, the financing of the Merger, the refinancing of certain of Parent’s debts and other transactions contemplated (the “Transactions”) by the Merger Agreement that the waiver and amendments (the “Amendments”) set forth in Articles 2 and 3 of this First Supplemental Indenture shall have been approved by Holders of not less than a majority of the outstanding principal amount of the Securities and a supplemental indenture in respect thereof shall have been executed and delivered by the Company and the Trustee, shall be binding and enforceable against the Holders of the outstanding Securities, and shall not have been modified, rescinded, terminated or superseded as of the closing of the Merger;

WHEREAS, the Company has received the consents from Holders of not less than a majority of the outstanding aggregate principal amount of the Securities, to effect the Amendments;

WHEREAS, the Company has delivered to the Trustee an Officer’s Certificate as well as an Opinion of Counsel pursuant to Sections 4.11, 11.6 and 12.4 of the Indenture to the effect that the execution and delivery of this First Supplemental Indenture by the Company is authorized and permitted under the Indenture and that all conditions precedent provided for in the Indenture to the execution and delivery of this First Supplemental Indenture to be complied with by the Company have been complied with;

WHEREAS, all other acts and proceedings required by law, by the Indenture and by the charter documents of the Company to make this First Supplemental Indenture a valid and binding agreement for the purposes expressed herein, in accordance with its terms, have been duly done and performed; and

WHEREAS, pursuant to Section 4.11 of the Indenture it is a condition precedent to any merger to which the Company is a party (other than a merger in which the Company is the continuing corporation and which does not result in any reclassification or change in outstanding shares of the Company’s Common Stock) that the Company execute and deliver to the Trustee a supplemental indenture setting forth the effect of such merger on the Holders’ conversion privilege as provided in Section 4.11;

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NOW, THEREFORE, in consideration of the premises, agreements and obligations set forth herein and for other good and valuable consideration, the receipt and sufficiency of which are hereby acknowledged, the parties hereto hereby agree as follows:

ARTICLE 1

RELATION TO INDENTURE; DEFINITIONS

SECTION 1.01. Relation to Indenture.

This First Supplemental Indenture constitutes an integral part of the Indenture.

SECTION 1.02. Definitions.

For all purposes of this First Supplemental Indenture, capitalized terms used herein and not otherwise defined herein shall have the meanings assigned thereto in the Indenture. In the event that any term contained herein shall conflict or be inconsistent with any defined term in the Indenture, the term as defined in this First Supplemental Indenture shall control.

SECTION 1.03. General References.

All references in this First Supplemental Indenture to Articles and Sections, unless otherwise specified, refer to the corresponding Articles and Sections of this First Supplemental Indenture; and the terms “herein”, “hereof”, “hereunder” and any other word of similar import refers to this First Supplemental Indenture.

ARTICLE 2

WAIVER OF CERTAIN INDENTURE PROVISIONS

SECTION 2.01. Waiver of Section 6.11.

The application of the covenant in Section 6.11 of the Indenture is hereby irrevocably waived with respect to (i) any Indebtedness, including any Acquired Indebtedness, that is incurred, guaranteed or assumed by the Company, Parent or any of their respective Subsidiaries upon or substantially contemporaneous with the consummation of the Transactions and (ii) any Liens that are granted by such Persons in connection with any such Indebtedness.

ARTICLE 3

AMENDMENTS TO INDENTURE

SECTION 3.01. Amendments to Table of Contents.

The Table of Contents of the Indenture is hereby amended by deleting the titles to Sections 6.2, 6.5, 6.6 and 6.11 and inserting in lieu thereof the phrase “[intentionally omitted]”.

SECTION 3.02. Elimination of Certain Definitions in Article One.

Section 1.02 of the Indenture is hereby amended by deleting the definitions “Acquired Indebtedness”; “Disqualified Equity Interest”; “EBITDA”; “Indebtedness”; “Interest Expense”; “Liens”; “maximum fixed repurchase price”; “Net Income”; “Permitted Indebtedness”; “Permitted Purchase Money Security Interest”; “Permitted Refinancing Indebtedness”; “Secured Date”; and “Weighted Average Life to Maturity” contained therein in their entirety.

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SECTION 3.03. SEC Reports.

Section 6.2 of the Indenture (SEC Reports) is hereby amended by deleting it in its entirety and replacing it with the following: “Section 6.2 [Intentionally omitted]”.

SECTION 3.04. Maintenance of Corporate Existence.

Section 6.5 of the Indenture (Maintenance of Corporate Existence) is hereby amended by deleting it in its entirety and replacing it with the following: “Section 6.5 [Intentionally omitted]”.

SECTION 3.05. Rule 144A Information Requirement.

Section 6.6 of the Indenture (Rule 144A Information Requirement) is hereby amended by deleting it in its entirety and replacing it with the following: “Section 6.6 [Intentionally omitted]”.

SECTION 3.06. Incurrence of Indebtedness.

Section 6.11 of the Indenture (Incurrence of Indebtedness) is hereby amended by deleting it in its entirety and replacing it with the following: “Section 6.11 [Intentionally omitted]”.

SECTION 3.07. Company May Consolidate, Etc., Only on Certain Terms.

Section 7.1 of the Indenture (Company May Consolidate, Etc., Only on Certain Terms) is hereby amended by deleting sub-section 7.1(3) in its entirety and replacing it with the following: “(3) [Intentionally omitted]”.

SECTION 3.08. Events of Default.

Section 8.1 of the Indenture (Events of Default) is hereby amended by deleting sub-sections 8.1(a)(5) (Failure to Perform Other Covenants), 8.1(a)(6) (Cross Default/Acceleration) and 8.1(a)(7) (Judgments) in their entirety and replacing them with the following: “[intentionally omitted]”.

ARTICLE 4

EFFECT OF MERGER ON CONVERSION PRIVILEGE

From and after the Effective Time (as defined below), the Holder of each Security then outstanding shall have the right pursuant to the procedures provided in the Indenture to convert such Security solely into cash, and any portion of the Conversion Obligation in excess of the principal amount of Securities being converted or Make-Whole Premium that a Holder is entitled to receive upon conversion in connection with the Transactions shall not be payable in shares of Common Stock but will represent a right to receive the amount of cash receivable upon the consummation of the Transactions by the holder of the shares of Common Stock otherwise issuable upon such conversion had such additional shares of Common Stock been outstanding immediately prior to the consummation of the Transactions.

ARTICLE 5

MISCELLANEOUS

SECTION 5.01. Effectiveness of First Supplemental Indenture.

This First Supplemental Indenture shall become effective immediately upon its execution and delivery, but the Amendments set forth in Articles Two through Four, inclusive, hereof will only become operative (a) contemporaneously with the filing of that certain Certificate of Merger (which is prepared in

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connection with the Merger Agreement (the “Certificate of Merger”)) with the Secretary of State of Delaware or (b) on such later effective date and/or time, if any, specified in such Certificate of Merger (such applicable time, the “Effective Time”). If the Effective Time has not occurred prior to February 11, 2009, Articles Two through Four, inclusive, of this First Supplemental Indenture shall not become operative. The Company shall provide a certified copy of the Certificate of Merger to the Trustee promptly following its filing with the Secretary of State of Delaware. If such Certificate of Merger has not been filed prior to February 11, 2009, the Company shall promptly, following February 11, 2009, provide written notice to the Trustee that Articles Two through Four, inclusive, of this First Supplemental Indenture have not become operative.

SECTION 5.02. Certain Trustee Matters.

The recitals contained herein shall be taken as the statements of the Company, and the Trustee assumes no responsibility for their correctness.

The Trustee makes no representations as to the validity or sufficiency of this First Supplemental Indenture or the proper authorization or the due execution hereof by the Company.

SECTION 5.03. Further Assurances.

Each of the parties hereto agrees that it shall, upon the reasonable request of the other party hereto (and not in contravention with the terms and conditions of the Indenture), execute and deliver any and all instruments and documents and take such additional action as the other party hereto may reasonably request to effect, consummate, confirm or evidence the transactions described herein promptly upon such other party’s request therefor.

SECTION 5.04. Continued Effect.

Except as expressly supplemented and amended by this First Supplemental Indenture, the Indenture shall continue in full force and effect in accordance with the provisions thereof, and the Indenture as heretofore amended, supplemented or otherwise modified, and as supplemented and amended by this First Supplemental Indenture, is in all respects hereby ratified and confirmed. This First Supplemental Indenture and all its provisions shall be deemed a part of the Indenture in the manner and to the extent herein and therein provided.

SECTION 5.05. Governing Law.

THIS FIRST SUPPLEMENTAL INDENTURE SHALL BE GOVERNED BY AND CONSTRUED IN ACCORDANCE WITH THE LAWS OF THE STATE OF NEW YORK, WITHOUT GIVING EFFECT TO THE CONFLICT OF LAWS PRINCIPLES THEREOF (EXCEPT SECTION 5-1401 OF THE NEW YORK GENERAL OBLIGATIONS LAW).

SECTION 5.06. Trust Indenture Act Controls.

If any provision of this First Supplemental Indenture limits, qualifies or conflicts with another provision of this First Supplemental Indenture or the Indenture that is required to be included by the Trust Indenture Act of 1939 as in force at the date as of which this First Supplemental Indenture is executed, the provision required by said Act shall control.

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SECTION 5.07. Trustee Disclaimer.

The recitals contained in this First Supplemental Indenture shall be taken as the statements of the Company, and the Trustee assumes no responsibility for their correctness. The Trustee makes no representations as to the validity or sufficiency of this First Supplemental Indenture. All rights, protections, privileges, indemnities and benefits granted or afforded to the Trustee under the Indenture shall be deemed incorporated herein by this reference and shall be deemed applicable to all actions taken, suffered or omitted by the Trustee under this First Supplemental Indenture.

SECTION 5.08. Counterparts; Facsimile or Electronic Signatures.

This First Supplemental Indenture may be executed in any number of counterparts, each of which shall be deemed to be an original, but all such counterparts shall together constitute but one and the same agreement. Delivery of an executed signature page of this First Supplemental Indenture by facsimile or electronic transmission shall be effective as delivery of a manually executed counterpart thereof and may be used for all purposes. Signatures of the parties transmitted by facsimile or electronic transmission shall be deemed to be their original signatures for all purposes.

SECTION 5.09. Amendments.

This First Supplemental Indenture may not be amended, waived, supplemented or otherwise modified except by an agreement in writing signed by each of the parties hereto.

SECTION 5.10. Severability.

If any provision of this First Supplemental Indenture is found by any court of competent jurisdiction to be invalid, illegal or unenforceable, such provision shall be deemed, as to such jurisdiction, to be modified to the minimum extent necessary to cause it to be valid, legal and enforceable and the invalidity, illegality or unenforceability of such provision prior to such modification shall not affect the other provisions of this First Supplemental Indenture and all provisions not affected by the invalidity, illegality or unenforceability shall remain in full force and effect; and the invalidity of a particular provision in a particular jurisdiction shall not invalidate such provision in any other jurisdiction.

[Signature Page Follows]

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

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