THIRD SUPPLEMENT TO THE PURCHASE CONTRACT AGREEMENT AMONG

Exhibit 4.12

THIRD SUPPLEMENT

TO THE

PURCHASE CONTRACT AGREEMENT

AMONG

NEW ALBERTSON’S, INC.,

SUPERVALU INC.

AND

U.S. BANK TRUST NATIONAL ASSOCIATION,

AS PURCHASE CONTRACT AGENT

THIS THIRD SUPPLEMENT TO THE PURCHASE CONTRACT AGREEMENT, dated as of June 2, 2006 (this “Supplemental Agreement”), New Albertson’s, Inc., a Delaware corporation formerly known as New Aloha Corporation (the “Company”), SUPERVALU INC. (“Parent”), and U.S. Bank Trust National Association, acting as purchase contract agent for the Holders of Units from time to time (the “Agent”) pursuant to the Purchase Contract Agreement (as hereafter referred to);

WHEREAS, Albertson’s, Inc., a Delaware corporation (“Albertson’s”) and now a Delaware limited liability company known as Albertson’s LLC (“Albertson’s LLC”) and the Agent executed and delivered a Purchase Contract Agreement, dated as of May 7, 2004, which was supplemented by that First Supplement to the Purchase Contract Agreement, dated as of June 1, 2006 (the “First Supplement”), among Albertson’s LLC, the Company and the Agent, and that Second Supplement to the Purchase Contract Agreement, dated as of June 1, 2006 (the “Second Supplement”) among Albertson’s LLC, the Company and the Agent (as so supplemented, the “Purchase Contract Agreement”), to provide for the execution and delivery of the Purchase Contracts and Certificates related to the Corporate Units and the Treasury Units (collectively, the “Units”);

WHEREAS, the First Supplement made provision with respect to the rights of the Holders pursuant to the requirements of Section 5.04(b) of the Purchase Contract Agreement;

WHEREAS, Albertson’s has filed a Certificate of Conversion with the Secretary of State of the state of Delaware, pursuant to which it has converted from a Delaware corporation into Albertson’s LLC (such conversion the “Conversion”);

WHEREAS, as a result of the Conversion and without need for any further action, the Purchase Contracts and the Purchase Contract Agreement became the continuing obligations of the Company;

WHEREAS, the Second Supplement evidenced the succession of the Company to Albertson’s LLC, and the assumption by the Company of the covenants of Albertson’s LLC in the Purchase Contract Agreement and in the Certificates;

WHEREAS, the Company and Parent are parties to that Agreement and Plan of Merger, dated as of January 22, 2006, by and between Parent, Emerald Acquisition Sub, Inc. (“Acquisition Sub”), Albertson’s, the Company, and New Diamond Sub, Inc. (the “Merger Agreement”);

WHEREAS, pursuant to the terms of the Merger Agreement, Acquisition Sub, a wholly-owned subsidiary of Parent, shall merge with and into the Company with the Company being the surviving corporation (the “Emerald Merger”);

WHEREAS, the Merger Agreement provides that, at the effective time of the Emerald Merger (the “Effective Time”), each share of Common Stock of the Company issued and outstanding immediately prior to the Effective Time (except for shares cancelled pursuant to Section 3.2(b) of the Merger Agreement) will be converted into, and will be cancelled in exchange for, the right to receive $20.35 in cash and 0.1820 shares of common stock of Parent, par value $1.00 per share (“Parent Common Stock”) (and cash in lieu of fractional shares pursuant to Section 3.6(h) of the Merger Agreement);

WHEREAS, Section 9.01 of the Purchase Contract Agreement permits the Company to merge with another corporation provided certain terms and conditions are satisfied;

WHEREAS, the Emerald Merger results in the occurrence of a Reorganization Event;

WHEREAS, Section 5.04(b)(i) of the Purchase Contract Agreement provides that in the event of a Reorganization Event the Person formed thereby shall execute and deliver to the Agent an agreement supplemental to the Purchase Contract Agreement providing that each Holder of each Outstanding Unit shall have the rights provided by Section 5.04(b)(i) of the Purchase Contract Agreement and for adjustments for subsequent events that are as nearly equivalent as may be practicable to the adjustments provided for in Section 5.04(b)(i) of the Purchase Contract Agreement;

WHEREAS, Section 8.01 of the Purchase Contract Agreement authorizes the Company and the Agent to enter into a supplemental agreement without the consent of any Holders to, among other things, make provision with respect to the rights of Holders pursuant to the requirements of Section 5.04(b) of the Purchase Contract Agreement;

WHEREAS, Parent and the Company have requested that the Agent execute and deliver this Supplemental Agreement; and

NOW THEREFORE, in consideration of their mutual promises, Parent and Company covenant and agree with the Agent as follows:

ARTICLE I

DEFINITIONS

Section 1.1 Definition of Terms. Unless the context otherwise requires:

(a) a term defined in the Purchase Contract Agreement has the same meaning when used in this Supplemental Agreement;

(b) a term defined anywhere in this Supplemental Agreement has the same meaning throughout;

(c) the singular includes the plural and vice versa; and

(d) headings are for convenience of reference only and do not affect interpretation.

ARTICLE II

CONCERNING THE EMERALD MERGER

Section 2.1 Parent as Issuer of Common Stock upon Settlement.

(a) From and after the Effective Time, the Company shall deliver an amount of cash, and the Company shall cause Parent to issue and deliver, and Parent agrees to so issue and deliver, the number of shares of Parent Common Stock, which together are sufficient to settle the Purchase Contracts as provided in Article III of this Supplemental Agreement, against payment in full of the Purchase Price in the manner set forth in the Purchase Contract Agreement and Section 2.1(b) hereof.

(b) The Company hereby agrees that it will immediately forward to Parent all funds received by it under Sections 5.02, 5.04(b)(ii), 5.07 or otherwise under the Purchase Contract Agreement for payment of the Purchase Price upon settlement of each Purchase Contract, in excess of the amount of cash to be delivered by the Company upon such settlement, for the shares of Parent Common Stock to be so issued.

(c) Subject to the other provisions of this Supplemental Agreement other than Section 2.1(d), from and after the Effective Time, references in the Purchase Contract Agreement to delivery, receipt, issuance, purchase or sale of Common Stock in connection with the settlement of Purchase Contracts or to the Purchase Price to be paid in respect of any Purchase Contracts for Common Stock shall by operation of Section 5.04(b)(i) of the Purchase Contract Agreement relate to the delivery, receipt, issuance, purchase or sale of cash and Parent Common Stock or to the Purchase Price to be paid in respect of any Purchase Contracts for cash and Parent Common Stock, to the extent necessary to give effect to Section 2.1(a) and Article III hereof.

(d) Subject to the other provisions of this Supplemental Agreement, from and after the Effective Time, references to the Common Stock shall relate to Parent Common Stock by operation of Section 5.04(b)(i) of the Purchase Contract Agreement, except to the extent that such reference is a reference to the Common Stock as of a time preceding the Effective Time.

(e) Subject to the other provisions of this Supplemental Agreement, from and after the Effective Time, any reference in the Purchase Contract Agreement to the “Company” shall be deemed to be a reference to Parent, and all covenants of the Company shall be deemed to be covenants of Parent, in each case to the extent necessary to give effect to Section 5.04(b) of the Purchase Contract Agreement and this Supplemental Agreement;

(f) Subject to the other provisions of this Supplemental Agreement, from and after the Effective Time, all references in Section 5.04(a)(xi) of the Purchase Contract Agreement to the Rights Agreement dated as of December 9, 1996, as amended, with American Stock Transfer & Trust Company shall be taken to be references to the Rights Agreement, dated as of April 12, 2000, between Parent and Wells Fargo Bank Minnesota, N.A., as amended (formerly Norwest Bank Minnesota, N.A.) as Rights Agent.

Section 2.2 Acceptance by Agent. The Agent accepts this Supplemental Agreement and agrees to execute its duties and responsibilities as hereby supplemented upon the terms and conditions set forth in the Purchase Contract Agreement, including without limitation the terms and provisions defining and limiting the liabilities and responsibilities of the Agent, which terms and provisions shall in like manner define and limit its liabilities and responsibilities

in the performance of its duties created by the Purchase Contract Agreement as hereby supplemented; and without limiting the generality of the foregoing, the Company affirms its rights and responsibilities with respect to the Agent under Section 7.07(c) of the Purchase Contract Agreement.

ARTICLE III

CONCERNING SETTLEMENT

Section 3.1 Settlement Rate and Fixed Settlement Rates.

(a) Pursuant to 5.04(b)(i) of the Purchase Contract, the Settlement Rate is adjusted such that from and after the Effective Time, the Settlement Rate equals:

(i) if the Adjusted Applicable Market Value is greater than or equal to $46.54, $17.65 in cash plus 0.1579 shares of Parent Common Stock.

(ii) if the Adjusted Applicable Market Value is less than the Threshold Appreciation Price but greater than $14.89, an amount of cash and a number of shares of Parent Common Stock in a ratio of $20.35 of cash to 0.1820 shares of Parent Common Stock, such that the sum of (A) the amount of such cash plus (B) the product of such number of shares times the Adjusted Applicable Market Value, is equal to the Stated Amount.

(iii) if the Adjusted Applicable Market Value is less than or equal to the Reference Price, $22.06 in cash plus 0.1973 shares of Parent Common Stock.

In each case rounded upward or downward to, in the case of shares of Parent Common Stock, the nearest 1/10,000th of a share, and in the case of cash, the nearest $0.01.

The Threshold Appreciation Price, Minimum Share Number, Reference Price and Maximum Share Number are adjusted accordingly, such that the Threshold Appreciation Price equals $46.54, the Minimum Share Number equals 0.1579 shares of Parent Common Stock, the Reference Price equals $14.89, and the Maximum Share Number equals 0.1973 shares of Parent Common Stock.

(b) The Early Settlement Rate is adjusted such that upon Early Settlement of Purchase Contracts by a Holder of the related Units, Parent shall issue, and the Holder shall be entitled to receive, 0.1579 shares of newly issued Parent Common Stock, and the Company shall deliver, and the Holder shall be entitled to receive, $17.65 in cash.

(c) Section 5.04(b)(ii) of the Purchase Contract Agreement is amended such that upon Cash Merger Early Settlement by a Holder, the Company will deliver or will cause the Collateral Agent to deliver to the Holder on the Cash Merger Early Settlement Date, in addition to those items provided for in the last three paragraphs (A), (B) and (C) of such Section 5.04(b)(ii) (with the reference to Common Stock in such paragraph (A) taken to be a reference

to Parent Common Stock), the amount of cash that would be deliverable on account of each Purchase Contract if the Purchase Contract Settlement Date had occurred immediately prior to such Cash Merger (based on the Settlement Rate in effect at such time).

Section 3.2 Purchase Contract Settlement. The Company and Parent understand and agree that, pursuant to 5.04(b)(i) of the Purchase Contract, implemented by Section 3.1 hereof as of the Effective Time, the Settlement Rate was adjusted such that each Holder of Units will receive on the Purchase Contract Settlement Date, any Cash Merger Early Settlement Date, or any Early Settlement Date, the amount of Exchange Property provided for in Section 5.04(b)(i), subject to any further adjustments in the Settlement Rate under Article V of the Purchase Contract Agreement prior to settlement, in all cases deeming all references to the Company’s Common Stock pertaining to a time after the Effective Time to be references to Parent Common Stock, and deeming all references to the Company pertaining to a time after the Effective Time to be references to Parent. The Company shall, within 10 Business Days following the Emerald Merger, (a) deliver to the Agent an Officers’ Certificate pursuant to Section 5.05(a)(i) of the Purchase Contract Agreement, which shall set forth the method of calculation of the Settlement Rate as of the Effective Time, as adjusted for the Emerald Merger, and (b) provide a written notice to Holders of the Units, pursuant to Section 5.05(a)(ii) of the Purchase Contract Agreement.

Section 3.3 Rights of Holders. Each Holder of an Outstanding Unit shall have the rights provided by Section 5.04(b)(i) of the Purchase Contract Agreement.

Section 3.4 Further Adjustments. In accordance with the last paragraph of Section 5.4(b)(i) of the Purchase Contract Agreement, the Settlement Rate shall be adjusted for events subsequent to the Effective Time, in a manner that is as nearly equivalent as may be practicable to the adjustments provided for in Section 5.04 of the Purchase Contract Agreement, as if Parent was the original “Company” and Parent Common Stock was the original “Common Stock” under the provisions of Section 5.04 of the Purchase Contract Agreement.

ARTICLE IV

MISCELLANEOUS

Section 4.1 Ratification of Purchase Contract Agreement. The Purchase Contract Agreement, as supplemented by this Supplemental Agreement, is in all respects ratified and confirmed, and this Supplemental Agreement shall be deemed part of the Purchase Contract Agreement in the manner and to the extent herein and therein provided.

Section 4.2 Effectiveness. This Supplemental Agreement shall become a legally effective and binding instrument upon the execution and delivery hereof by all parties hereto.

Section 4.3 Purchase Contract Agreement. Except as supplemented hereby, all provisions in the Purchase Contract Agreement shall remain in full force and effect.

Section 4.4 Third Party Rights. Nothing in this Supplemental Agreement or the Units, express or implied, shall give to any Person, other than the parties hereto and thereto and their successors hereunder and thereunder and the Holders of the Units, any benefit of any legal or equitable right, remedy or claim under the Purchase Contract Agreement, this Supplemental Agreement or the Units.

Section 4.5 Successors. All agreements of the Company and Parent in this Supplemental Agreement shall bind their respective successors and assigns, whether so expressed or not.

Section 4.6 Recitals. The recitals and statements herein contained are made by the Company and Parent and not by the Agent, and the Agent assumes no responsibility for the correctness thereof. The Agent makes no representations as to the validity or sufficiency of this Supplemental Agreement.

Section 4.7 Units Deemed Conformed. As of the Effective Time, the provisions of each Unit then outstanding shall be deemed to be conformed, without the necessity for any reissuance or exchange of such Unit or any other action on the part of the Holders, Parent, the Company or Agent, so as to reflect this Supplemental Agreement.

Section 4.8 Governing Law. This Supplemental Agreement and the rights and obligations of the parties hereunder shall be governed by and construed in accordance with the laws of the State of New York.

Section 4.9 Separability. If any one or more of the provisions contained in this Supplemental Agreement or in the Units shall for any reason be held to be invalid, illegal or unenforceable in any respect, such invalidity, illegality or unenforceability shall not affect any other provisions of this Supplemental Agreement or of the Units, but this Supplemental Agreement and the Units shall be construed as if such invalid or illegal or unenforceable provision had never been contained herein or therein.

Section 4.10 Counterparts. This Supplemental Agreement may be executed in any number of counterparts, all of which taken together shall constitute one and the same instrument.

[SIGNATURE PAGES FOLLOW]

IN WITNESS WHEREOF, this Third Supplement to the Purchase Contract Agreement is executed as of the date first set forth above.