Completion of Acquisition or Disposition of Assets

Exhibit 4.1

EXECUTION COPY

SPSS INC.

AND

WILMINGTON TRUST FSB
as Successor Trustee

FIRST SUPPLEMENTAL INDENTURE

Dated as of October 2, 2009

to

INDENTURE

Dated as of March 19, 2007

2.50% Convertible Subordinated Notes due 2012

     FIRST SUPPLEMENTAL INDENTURE, dated as of October 2, 2009 (the “First Supplemental Indenture”), between SPSS INC., a Delaware corporation (hereinafter called the “Company”), and WILMINGTON TRUST FSB, as successor trustee (hereinafter called the “Trustee”).

RECITALS

     WHEREAS, the Company executed and delivered to the LaSalle Bank National Association, as predecessor trustee to the Trustee, that certain Indenture, dated as of March 19, 2007 (the “Indenture”), pursuant to which the 2.50% Convertible Subordinated Notes of the Company (the “Notes”) were issued;

     WHEREAS, pursuant to the terms of the Indenture, the Notes are convertible into shares of common stock, par value $0.01 per share, of the Company (“Common Stock”);

     WHEREAS, pursuant to an Agreement and Plan of Merger, dated as of July 27, 2009 (the “Merger Agreement”), among the Company, International Business Machines Corporation, a New York corporation (“IBM”), and Pipestone Acquisition Corp., a Delaware corporation and a wholly owned subsidiary of IBM (“Merger Sub”), Merger Sub will merge with and into the Company (the “Merger”), with the Company as the surviving corporation and a wholly owned subsidiary of IBM, as a result of which each issued and outstanding share of Common Stock (other than shares of Common Stock held by the Company, IBM or Merger Sub) shall be converted into the right to receive $50.00 in cash, without interest and less any applicable withholding taxes (the “Merger Consideration”), and such shares of Common Stock shall no longer be outstanding and shall automatically be cancelled and cease to exist, and each holder of a certificate or evidence of shares in book-entry form that immediately prior to the effective time of the Merger represented any such shares shall cease to have any right with respect thereto, except the right to receive the Merger Consideration in accordance with the terms of the Merger Agreement;

     WHEREAS, Section 4.10 of the Indenture requires the Company to execute and deliver to the Trustee this First Supplemental Indenture in order to reflect the effect of the Merger on the holders of Common Stock; and

     WHEREAS, the consummation of the Merger shall constitute a Fundamental Change (as such term is defined in the Indenture).

     NOW, THEREFORE, in consideration of the premises, it is mutually agreed, for the equal and proportionate benefit of the respective Holders from time to time of the Notes, as follows:

ARTICLE ONE
CONCERNING THE NOTES

     Section 1.1. Conversion Privilege.

     Each Note outstanding after the Merger shall, from and after the effective time of this First Supplemental Indenture, during the period such Note shall be convertible as specified in Section 4.01(a) of the Indenture, be convertible into the right to receive, for each $1,000 principal amount of Notes surrendered for conversion, an amount of cash equal to $50.00 multiplied by the applicable Conversion Rate.

ARTICLE TWO
CONCERNING THE TRUSTEE

     Section 2.1. Terms and Conditions.

     The Trustee accepts this First Supplemental Indenture and agrees to perform the duties of the Trustee upon the terms and conditions herein and in the Indenture set forth.

     Section 2.2. No Responsibility.

     The Trustee makes no undertaking or representations in respect of, and shall not be responsible in any manner whatsoever for and in respect of, the validity or sufficiency of this First Supplemental Indenture or the proper authorization or the due execution hereof by the Company, or for or in respect of the recitals and statements contained herein, all of which recitals and statements are made solely by the Company.

ARTICLE THREE
EFFECT OF EXECUTION AND DELIVERY HEREOF

     From and after the effective time of this First Supplemental Indenture, (i) the Indenture shall be deemed to be amended and modified as provided herein, (ii) this First Supplemental Indenture shall form a part of the Indenture, (iii) except as modified and amended by this First Supplemental Indenture, the Indenture shall continue in full force and effect, (iv) the Notes shall continue to be governed by the Indenture, as modified and amended by this First Supplemental Indenture, and (v) every Holder of Notes heretofore and hereafter authenticated and delivered under the Indenture shall be bound by this First Supplemental Indenture.

ARTICLE FOUR
MISCELLANEOUS PROVISIONS

     Section 4.1. Effective Time.

     This First Supplemental Indenture is effective as of the Effective Time of the Merger, as defined in the Merger Agreement.

     Section 4.2. Headings Descriptive.

     The headings of the several Articles and Sections of this First Supplemental Indenture are inserted for convenience only and shall not in any way affect the meaning or construction of any provision of this First Supplemental Indenture.

     Section 4.3. Rights and Obligations of the Trustee.

     All of the provisions of the Indenture with respect to the rights, privileges, immunities, powers and duties of the Trustee shall be applicable in respect of this First Supplemental Indenture as fully and with the same effect as if set forth herein in full.

     Section 4.4. Successors and Assigns.

     This First Supplemental Indenture shall be binding upon and inure to the benefit of and be enforceable by the respective successors and assigns of the parties hereto and the Holders of any Notes then outstanding.

     Section 4.5. Defined Terms

     Capitalized terms used in this First Supplemental Indenture and not defined herein shall have the meanings ascribed to such terms in the Indenture.

     Section 4.6. Counterparts.

     This First Supplemental Indenture may be executed in several counterparts, each of which shall be an original and all of which shall constitute but one and the same instrument.

     Section 4.7. Governing Law.

     This First Supplemental Indenture shall be governed by and construed in accordance with the laws of the State of New York.

     Section 4.8. Separability.

     If any provision in this First Supplemental Indenture shall be invalid, illegal or unenforceable, the validity, legality and enforceability of the remaining provisions shall not in any way be affected or impaired thereby.

     Section 4.9. Trust Indenture Act.

     If and to the extent that any provision of this First Supplemental Indenture limits, qualifies or conflicts with another provision which is required to be included in this First Supplemental Indenture or in the Indenture by the Trust Indenture Act of 1939, as amended (the “TIA”), such required provision of the TIA shall control.

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