BJS WHOLESALE CLUB, INC. AMENDMENT NO. 1 TO CHANGE INCONTROL SEVERANCE AGREEMENT

Exhibit 10.20b

BJ’S WHOLESALE CLUB, INC.

AMENDMENT NO. 1 TO CHANGE IN CONTROL SEVERANCE AGREEMENT

This Amendment No. 1 to Change in Control Severance Agreement (the “Amendment”) between BJ’s Wholesale Club, Inc. (the “Company”) and Cornel Catuna (“Executive”) is made as of March 24, 2011.

WHEREAS, the Company and Executive entered into a Change in Control Severance Agreement dated January 30, 2011 (as so amended, the “Agreement”).

WHEREAS, the parties desire to further amend the Agreement to provide that the “excess parachute payment” excise tax cut-back provisions included in the Agreement will apply only if Executive would be better off on an after-tax basis after such cut-back.

NOW, THEREFORE, for valuable consideration, receipt of which is acknowledged, the parties agree as follows:

1. Section 1.3 of the Agreement is deleted in its entirety and replaced by the following:

“Coordination With Certain Tax Rules.

In the event that the Company undergoes a Change in Ownership or Control (as defined below), the Company shall not be obligated to provide to Executive a portion of any Contingent Compensation Payments (as defined below) that Executive would otherwise be entitled to receive to the extent necessary to eliminate any Excess Parachute Payments (as defined below) for Executive. For purposes of this Section 1.3, the Contingent Compensation Payments so eliminated shall be referred to as the “Eliminated Payments” and the aggregate amount (determined in accordance with Treasury Regulation Section 1.280G-1, Q/A-30 or any successor provision) of the Contingent Compensation Payments so eliminated shall be referred to as the “Eliminated Amount.” Notwithstanding any other provision of this Agreement, if the Eliminated Amount for Executive equals or exceeds the sum of:

(i) the Threshold Amount (as defined below), plus

(ii) the Income Tax Payable on the Eliminated Amount (as defined below), plus

(iii) the Excise Tax Payable on Excess Parachute Payments (as defined below), no portion of any Contingent Compensation Payments shall be eliminated for Executive.

For purposes of this Section 1.3, the following terms shall have the following respective meanings:

“Change in Ownership or Control” shall mean a change in the ownership or effective control of the Company or in the ownership of a substantial portion of the assets of the Company determined in accordance with Section 280G(b)(2) of the Code.

“Contingent Compensation Payments” shall mean any payment (or benefit) in the nature of compensation that is made or made available (under this Agreement or otherwise) to a “disqualified individual” (as defined in Section 280G(c) of the Code) and that is contingent (within the meaning of Section 280G (b) (2) (A) (i) of the Code) on a Change in Ownership or Control of the Company.

“Excess Parachute Payments” shall mean “excess parachute payments” as defined in Section 280G(b)(1) of the Code before taking into account the Eliminated Amount, if otherwise applicable.

“Threshold Amount” shall mean $25,000.

“Income Tax Payable on the Eliminated Amount” shall mean the Eliminated Amount (determined without regard to whether any Contingent Compensation Payments are actually eliminated) multiplied by the highest combined marginal federal, state and local income tax rate in effect for the taxable year, taking into account the phase-out of itemized deductions and the federal Medicare tax.

“Excise Tax Payable on Excess Parachute Payments” shall mean the tax imposed by Section 4999(a) of the Code on Excess Parachute Payments.

Within 45 days after each date on which Executive first becomes entitled to receive (whether or not then due) payments or benefits relating to a Change in Ownership or Control, the Company, at its expense, shall engage a nationally recognized law firm or a nationally recognized accounting firm, which may be the regular law firm or accounting firm of the Company (the “280G Firm”), to determine (i) which of such payments and benefits constitute Contingent Compensation Payments, (ii) the Eliminated Amount and (iii) the Eliminated Payments. To identify the Eliminated Payments, the 280G Firm shall determine the “Contingent Compensation Payment Ratio” (as defined below) for each Contingent Compensation Payment and then reduce the Contingent Compensation Payments in order beginning with the Contingent Compensation Payments with the highest Contingent Compensation Payment Ratio. For Contingent Compensation Payments with the same Contingent Compensation Payment Ratio, such Contingent Compensation Payments shall be reduced based on the time of payment of such Contingent Compensation Payments, with amounts having later payment dates being reduced first. For Contingent Compensation Payments with the same Contingent Compensation Payment Ratio and the same time of payment, such Contingent Compensation Payments shall be reduced on a pro rata basis (but not below zero) prior to reducing Contingent Compensation Payments with a lower Contingent Compensation Payment Ratio. The term “Contingent Compensation Payment Ratio” shall mean a fraction, the numerator of which is the value of the applicable Contingent Compensation Payment that must be taken into account at the change in control date for purposes of Section 280G of the Code, and the denominator of which is the present value at the change in control date of the actual amount to be received in respect of the applicable payment (e.g., in the case of equity grants, the denominator shall be determined by reference to the fair market value of the equity at the relevant dates and not in

accordance with the methodology for accelerated payments set forth in Treasury Regulation Section 1.280G-1Q/A 24(b) or (c)).

Within 30 days after each date on which Executive first becomes entitled to receive (whether or not then due) payments or benefits relating to such Change in Ownership or Control, the Company shall provide notice to Executive with reasonable detail of (i) which payments and benefits constitute Contingent Compensation Payments, (ii) the Eliminated Amount and (iii) the Eliminated Payments.

In the event of any underpayment or overpayment hereunder, as determined by the 280G Firm, the amount of such underpayment or overpayment shall within 30 days of such determination be paid to Executive or refunded to the Company, as the case may be, with interest at the applicable federal rate provided for in Section 7872(f)(2) of the Code.”

IN WITNESS WHEREOF, the parties hereto have executed this Amendment as of the date first above written.