FIRST SUPPLEMENTAL INDENTURE

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

-i-

-ii-

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;

-1-

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

R ELATION TO I NDENTURE ; D EFINITIONS

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

W AIVER OF C ERTAIN I NDENTURE P ROVISIONS

SE