SECOND SUPPLEMENT TO THE PURCHASE CONTRACT AGREEMENT AMONG ALBERTSON’S LLC, NEW ALBERTSON’S, INC. AND AS PURCHASE CONTRACT AGENT

Exhibit 4.11

SECOND SUPPLEMENT

TO THE

PURCHASE CONTRACT AGREEMENT

AMONG

ALBERTSON’S LLC,

NEW ▇▇▇▇▇▇▇▇▇’▇, INC.

AND

U.S. BANK TRUST NATIONAL ASSOCIATION,

AS PURCHASE CONTRACT AGENT

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THIS SECOND SUPPLEMENT TO THE PURCHASE CONTRACT AGREEMENT, dated as of June 1, 2006 (this “Supplemental Agreement”), among Albertson’s LLC, a Delaware limited liability company (the “Company”) and formerly a Delaware corporation known as ▇▇▇▇▇▇▇▇▇’▇, Inc. (“Albertson’s”), New ▇▇▇▇▇▇▇▇▇’▇, Inc., a Delaware corporation formerly known as New Aloha Corporation (“New Albertson’s”), 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 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, New Albertson’s 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 the Company (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, New Albertson’s has entered into that Purchase and Separation Agreement, dated as of January 22, 2006, by and among Albertson’s, New Albertson’s, SUPERVALU INC., and AB Acquisition LLC, as amended (the “Separation Agreement”);

WHEREAS, pursuant to the Separation Agreement, the Company shall have transferred substantially all of its properties and assets to New Albertson’s (such transfer, the “Separation”); and

WHEREAS, as a condition to the Separation, Section 901 of the Purchase Contract Agreement requires, among other things, that New Albertson’s execute and deliver one or more supplemental agreements to expressly assume all the obligations of the Company under the Purchase Contracts, the Purchase Contract Agreement, the Pledge Agreement, the Indenture (including any supplement thereto) and the Remarketing Agreement;

WHEREAS, New Albertson’s shall have expressly assumed such obligations pursuant to (1) this Supplemental Agreement; (2) that Supplemental Indenture No. 2, dated as of the date hereof (the “Indenture Supplement”), among the Company, New Albertson’s and U.S. Bank Trust National Association, as successor trustee; (3) that First Supplement to the Pledge Agreement, dated as of the date hereof (the “Pledge Supplement”), among the Company, New Albertson’s, the Agent and U.S. Bank Trust National Association, as collateral agent, custodial agent

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and securities intermediary; and (4) that Assignment and Assumption Agreement, dated as of the date hereof (the “Remarketing Supplement”), among the Company, New Albertson’s and Banc of America Securities LLC, as remarketing agent (such assumptions, the “Assumptions”);

WHEREAS, Section 8.01(a) of the Purchase Contract Agreement authorizes the Company and the Agent to enter into a supplemental agreement without the consent of any Holders to evidence the succession of another Person to the Company, and the assumption by any such successor of the covenants of the Company in the Purchase Contract Agreement and in the Certificates;

WHEREAS, New Albertson’s and Company desire to enter into a supplemental agreement pursuant to the terms of Sections 8.01(a) and 9.01 of the Purchase Contract Agreement;

WHEREAS, the New Albertson’s and the Company have requested that the Agent execute and deliver this Supplemental Agreement pursuant to the terms of Section 8.01(a) of the Purchase Contract Agreement; and

NOW THEREFORE, in consideration of their mutual promises, New Albertson’s and the 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

REPRESENTATIONS AND WARRANTIES

Section 2.1 Each of New Albertson’s and the Company represents and warrants that the Separation constitutes the transfer of all or substantially all the Company’s properties and assets to New Albertson’s.

Section 2.2 New Albertson’s represents and warrants that it is a corporation duly organized and validly existing under the laws of the State of Delaware.

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Section 2.3 Each of the Company and New Albertson’s represents and warrants that it has all requisite power and authority to execute, deliver and perform its obligations hereunder, and under the Purchase Contract Agreement, the Purchase Contracts, the Indenture, the Pledge Agreement and the Remarketing Agreement, in each case as amended and supplemented, and that the execution, delivery and performance by the Company and New Albertson’s of this Supplemental Agreement and the Purchase Contract Agreement have been duly authorized by all necessary corporate or other organizational action.

Section 2.4 Each of the Company and New Albertson’s represents and warrants that neither the Company nor New Albertson’s shall, immediately after the Separation, be in default of payment obligations under the Purchase Contracts, the Purchase Contract Agreement, the Pledge Agreement, the Indenture (including any supplement thereto) or the Remarketing Agreement or in material default in the performance of any other covenants under any of the foregoing agreements.

ARTICLE III

ASSUMPTION OF OBLIGATIONS

Section 3.1 Assumption. New Albertson’s hereby expressly assumes all the obligations of the Company under the Purchase Contracts and the Purchase Contract Agreement.

Section 3.2 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, New Albertson’s affirms as its own the rights and responsibilities of the Company with respect to the Agent under Section 7.07(c) of the Purchase Contract Agreement.

ARTICLE IV

SUCCESSION AND SUBSTITUTION

Section 4.1 Succession and Substitution. Upon the consummation of the Separation (the time at which such consummation occurs, the “Succession Time”), Section 9.02 of the Purchase Contract Agreement shall have effect to the extent set forth therein, subject to such Section.

Section 4.2 Notices. The address of the Company to which notices or communications to the Company are to be sent pursuant to Section 1.05 of the Purchase Contract Agreement shall be, from and after the date hereof,

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New ▇▇▇▇▇▇▇▇▇’▇, Inc.

c/o SUPERVALU INC.

▇▇▇▇▇ ▇▇▇▇▇▇ ▇▇▇▇ ▇▇▇▇

▇▇▇▇ ▇▇▇▇▇▇▇, ▇▇ ▇▇▇▇▇

FAX: (▇▇▇) ▇▇▇-▇▇▇▇

Attention: Treasurer

Section 4.3 Common Stock Prior to the Initial Effective Time. Notwithstanding anything to the contrary in this Supplemental Agreement, all references in the Purchase Contract Agreement to the “Common Stock” of the Company that relate to a time prior to the Initial Effective Time (as defined in the First Supplement), including any computation of the Adjusted Applicable Market Value pursuant to Section 5.01 of the Purchase Contract Agreement, shall be deemed to refer to the Common Stock of Albertson’s at such time.

ARTICLE V

CONCERNING THE FIRST SUPPLEMENT

Section 5.1 The Company and New Albertson’s agree that, subject to the other provisions of this Supplemental Agreement, from and after the Succession Time, Section 2.1(b) of the First Supplement shall have no further effect.

ARTICLE VI

CONCERNING SETTLEMENT

Section 6.1 Reorganization Event. To the extent that the Separation constitutes a Reorganization event, each Holder of an Outstanding Unit shall have the rights provided by Section 5.04(b)(i) of the Purchase Contract Agreement.

Section 6.2 No Adjustment. The Company and New Albertson’s understand and agree that, pursuant to Section 5.04(b)(i) of the Purchase Contract Agreement as supplemented by the First Supplement, the Separation does not constitute a Reorganization Event as a result of which the Settlement Rate is to be adjusted.

ARTICLE VII

MISCELLANEOUS

Section 7.1 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 7.2 Effectiveness. This Supplemental Agreement shall become a legally effective and binding instrument upon the execution and delivery hereof by all parties hereto.

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Section 7.3 Purchase Contract Agreement. Except as supplemented hereby, all provisions in the Purchase Contract Agreement shall remain in full force and effect.

Section 7.4 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 7.5 Successors. All agreements of the Company and New Albertson’s in this Supplemental Agreement shall bind their respective successors and assigns, whether so expressed or not.

Section 7.6 Recitals. The recitals and statements herein contained are made by the Company and New Albertson’s 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 7.7 Units Deemed Conformed. As of the Succession 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, New Albertson’s, the Company or Agent, so as to reflect this Supplemental Agreement.

Section 7.8 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 7.9 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 7.10 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]

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