Exhibit 4.1

AMENDMENT NO. 1 TO THE

RIGHTS AGREEMENT

This Amendment No. 1 (this “Amendment”) is dated as of May 29, 2018, and amends that certain Rights Agreement, dated as of May 17, 2018, (the “Rights Agreement”), between Essendant Inc., a Delaware corporation (the “Company”), and Equiniti Trust Company, a limited trust company organized under the laws of the State of New York (the “Rights Agent”). Capitalized terms used herein and not otherwise defined shall have the meaning ascribed to them in the Rights Agreement.

WHEREAS, on May 29, 2018, the Board determined it is in the best interests of the Company and its stockholders to amend the Rights Agreement on the terms set forth herein;

WHEREAS, in accordance with Section 27 of the Rights Agreement, prior to the Distribution Date, the Company and the Rights Agent shall, if the Company so directs, from time to time supplement or amend the Rights Agreement without the approval of any holders of shares of Common Stock;

WHEREAS, the Rights Agent is hereby directed to join in this Amendment; and

WHEREAS, an officer of the Company has delivered to the Rights Agent a certificate as to the compliance of this Amendment with the terms of Section 27 of the Rights Agreement.

NOW, THEREFORE, in consideration of the premises and the respective agreements set forth herein, the parties hereby agree as follows:

1. Amendment of the Rights Agreement.

“Exempt Person” shall mean any Person who or which, together with all Affiliates and Associates of such Person, is, as of midnight at the end of May 17, 2018, New York City time, the Beneficial Owner of ten percent (10%) or more of the shares of Common Stock then outstanding. Notwithstanding anything to the contrary provided in this Agreement, any Exempt Person who, together with such Person’s Affiliates and Associates, after midnight at the end of May 17, 2018, New York City time, becomes the Beneficial Owner of less than ten percent (10%) of the shares of Common Stock then outstanding shall cease to be an Exempt Person and shall be subject to all the provisions of this Agreement in the same manner as any Person who is not and was not an Exempt Person.

2. No Other Amendment; Effect of Amendment. Except as and to the extent expressly modified by this Amendment, the Rights Agreement and the exhibits thereto shall remain in full force and effect in all respects without any modification. This Amendment shall be deemed to be an amendment to the Rights Agreement effective retroactively to the date and time of the execution and delivery of the Rights Agreement, and the Rights Agreement shall be interpreted and construed as if the provisions of the Rights Agreement as amended by this Amendment had been the provisions of the Rights Agreement at all times that the Rights Agreement has been in effect.

3. Counterparts. This Amendment may be executed in any number of counterparts and each of such counterparts shall for all purposes be deemed to be an original, and all such counterparts shall together constitute but one and the same instrument. A signature to this Amendment transmitted electronically shall have the same authority, effect and enforceability as an original signature.

4. Governing Law. This Amendment shall be deemed to be a contract made under the laws of the State of Delaware and for all purposes shall be governed by and construed in accordance with the laws of such State applicable to contracts made and to be performed entirely within such State; provided, however, that all provisions regarding the rights, duties and obligations of the Rights Agent shall be governed by and construed in accordance with the laws of the State of New York applicable to contracts made and to be performed entirely within the State of New York, without regard to the principles or rules concerning conflicts of laws which might otherwise require application of the substantive laws of another jurisdiction.

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IN WITNESS WHEREOF, the parties hereto have executed this Amendment No. 1 to the Rights Agreement as of the date first above written.

[Signature Page to Amendment No. 1 to the Rights Agreement]

[Signature Page to Amendment No. 1 to the Rights Agreement]

Exhibit A

FORM OF

SUMMARY OF RIGHTS TO PURCHASE

PREFERRED STOCK

On May 17, 2018, the Board of Directors (the “Board”) of Essendant Inc., a Delaware corporation (the “Company”) authorized and declared a dividend distribution of one right (a “Right”) for each outstanding share of common stock of the Company, par value $0.10 per share (the “Common Stock”), to stockholders of record at the close of business on May 27, 2018 (the “Record Date”). Each Right entitles the registered holder to purchase from the Company a unit consisting of one one-thousandth of a share (a “Unit”) of a newly authorized series of Series A Junior Participating Preferred Stock, par value $0.01 per share (the “Preferred Stock”) at a purchase price of $33.00 per Unit, subject to adjustment (the “Purchase Price”). The description and complete terms of the Rights are set forth in a Rights Agreement, dated as of May 17, 2018, between the Company and Equiniti Trust Company, as rights agent (the “Rights Agreement”).

Rights Certificates; Exercise Period.

Initially, the Rights will be attached to all shares of Common Stock then outstanding, and no separate rights certificates (“Rights Certificates”) will be distributed. Subject to certain exceptions specified in the Rights Agreement, the Rights will separate from the Common Stock and the distribution date (the “Distribution Date”) will occur upon the earlier of (i) 10 business days following a public announcement that a person or group of affiliated or associated persons (an “Acquiring Person”) has acquired beneficial ownership of 10% (or 15% in the case of a “13G Institutional Investor,” as defined in the Rights Agreement) or more of the outstanding shares of Common Stock (the “Stock Acquisition Date”), other than as a result of repurchases of stock by the Company or certain inadvertent actions by certain stockholders, or (ii) 10 business days (or such later date as the Board shall determine) following the commencement of a tender offer or exchange offer that, if consummated, would result in a person or group becoming an Acquiring Person. For purposes of the Rights Agreement, beneficial ownership is defined to include ownership of derivative securities.

The Rights Agreement provides that no person or entity will become an Acquiring Person, and no Stock Acquisition Date or Triggering Event (as defined below) will occur, solely by reason of the (i) approval, execution, delivery, pendency, performance, public announcement or public disclosure of the Agreement and Plan of Merger (the “Merger Agreement”), dated as of April 12, 2018, by and among Genuine Parts Company (“GPC”), Rhino SpinCo, Inc., the Company and Elephant Merger Sub Corp., or any other Transaction Document (as defined in the Merger Agreement) (including any amendments, modifications or supplements thereto) or (ii) consummation of the merger of Elephant Merger Sub Corp. with and into Rhino SpinCo, Inc., or the consummation with GPC or any of its affiliates of any other transaction contemplated by the Transaction Documents. Additionally, the Rights Agreement provides that any person or group of affiliated or associated persons who, as of midnight at the end of May 17, 2018, New York City time, beneficially owns 10% or more of the outstanding shares of Common Stock (an “Exempt Person”) shall not be deemed an Acquiring Person, but only for so long as such person, together with its affiliates and associates, does not become the beneficial owner of any additional shares of Common Stock while such person is an Exempt Person.

Until a Distribution Date, (i) the Rights will be evidenced by the certificates for the Common Stock (or, in the case of shares reflected on the direct registration system, by the notations in the book-entry accounts) and will only be transferable with such Common Stock, (ii) new Common Stock certificates issued after the Record Date will contain a legend incorporating the Rights Agreement by reference, and (iii) the surrender for transfer of any certificates for Common Stock outstanding will also constitute the transfer of the Rights associated with the Common Stock represented by such certificates. Pursuant to the Rights Agreement, the Company reserves the right to require prior to the occurrence of a Triggering Event that, upon any exercise of Rights, a number of Rights be exercised so that only whole shares of Preferred Stock will be issued.

The Rights are not exercisable until a Distribution Date and will expire at 5:00 P.M., New York City time, on May 17, 2019, unless the Rights are earlier redeemed, exchanged or terminated.

As soon as practicable after a Distribution Date, Rights Certificates will be mailed to holders of record of the Common Stock as of the close of business on a Distribution Date and, thereafter, the separate Rights Certificates alone will represent the Rights. Except as otherwise determined by the Board, only shares of Common Stock issued prior to a Distribution Date will be issued with the Rights.

Flip-in Trigger.

In the event that a person or group of affiliated or associated persons becomes an Acquiring Person (unless the event causing such person or group to become an Acquiring Person is a transaction described under “Flip-over Trigger,” below), each holder of a Right will thereafter have the right to receive, upon exercise, Common Stock (or, in certain circumstances, cash, property or other securities of the Company) having a value equal to two times the exercise price of the Right. Notwithstanding the foregoing, following the occurrence of the event set forth in this paragraph, all Rights that are, or (under certain circumstances specified in the Rights Agreement) were, beneficially owned by any Acquiring Person will be null and void. However, Rights are not exercisable following the occurrence of the event set forth above until such time as the Rights are no longer redeemable by the Company as set forth below.

Flip-over Trigger.

In the event that, at any time following the Stock Acquisition Date, (i) the Company engages in a merger or other business combination transaction in which the Company is not the surviving corporation, (ii) the Company engages in a merger or other business combination transaction in which the Company is the surviving corporation and the Common Stock of the Company is changed or exchanged, or (iii) more than 50% of the Company’s assets, cash flow or earning power is sold or transferred, each holder of a Right (except Rights which have previously been voided as set forth above) shall thereafter have the right to receive, upon exercise, common stock of the acquiring company having a value equal to two times the exercise price of the Right. The events set forth in this paragraph and in the preceding paragraph are referred to as the “Triggering Events.”

Exchange Feature.

At any time after a person becomes an Acquiring Person and prior to the acquisition by any person or group of 50% or more of the outstanding Common Stock, the Board may exchange the Rights (other than Rights owned by such person or group which have become void), in whole or in part, at an exchange ratio of one share of Common Stock, or one one-thousandth of a share of Preferred Stock (or of a share of a class or series of the Company’s preferred stock having equivalent rights, preferences and privileges), per Right (subject to adjustment).

Equitable Adjustments.

The Purchase Price payable, and the number of Units of Preferred Stock or other securities or property issuable, upon exercise of the Rights are subject to adjustment from time to time to prevent dilution (i) in the event of a dividend on the Preferred Stock payable in shares of Preferred Stock, a subdivision or split of outstanding shares of Preferred Stock, a combination or consolidation of Preferred Stock into a smaller number of shares through a reverse stock split or otherwise, or reclassification of the Preferred Stock, (ii) if holders of the Preferred Stock are granted certain rights, options or warrants to subscribe for Preferred Stock or convertible securities at less than the current market price of the Preferred Stock, or (iii) upon the distribution to holders of the Preferred Stock of cash (excluding regular quarterly cash dividends), assets, evidences of indebtedness or of subscription rights or warrants (other than those referred to above).

With certain exceptions, no adjustment in the Purchase Price will be required until cumulative adjustments amount to at least 1% of the Purchase Price. No fractional Units will be issued and, in lieu thereof, an adjustment in cash will be made based on the market price of the Preferred Stock on the last trading date prior to the date of exercise.

Redemption Rights.

At any time until ten business days following the Stock Acquisition Date, the Company may redeem the Rights in whole, but not in part, at a price of $0.001 per Right (payable in cash, Common Stock or other consideration deemed appropriate by the Board). Immediately upon the action of the Board ordering redemption of the Rights, the Rights will terminate and the only right of the holders of Rights will be to receive the $0.001 redemption price.

Amendment.

Any of the provisions of the Rights Agreement may be amended by the Board prior to a Distribution Date. After a Distribution Date, the provisions of the Rights Agreement may be amended by the Board in order to cure any ambiguity, to correct or supplement any provision contained in the Rights Agreement that may be defective or inconsistent with any other provision therein, to make changes that do not adversely affect the interests of holders of Rights, or to shorten or lengthen any time period under the Rights Agreement. Notwithstanding the foregoing, no amendment may be made at such time as the Rights are not redeemable, except to cure any ambiguity or correct or supplement any provision contained in the Rights Agreement that may be defective or inconsistent with any other provision therein.

Miscellaneous.

Until a Right is exercised, the holder thereof, as such, will have no separate rights as a stockholder of the Company, including, without limitation, the right to vote or to receive dividends in respect of the Rights. While the distribution of the Rights will not be taxable to stockholders or to the Company, stockholders may, depending upon the circumstances, recognize taxable income in the event that the Rights become exercisable for Common Stock (or other consideration) of the Company or for common stock of the acquiring company or in the event of the redemption of the Rights as set forth above.

Anti-Takeover Effects.

The Rights may have certain anti-takeover effects. The Rights may cause substantial dilution to any person or group that attempts to acquire the Company without the approval of the Board. As a result, the overall effect of the Rights may be to render more difficult or discourage a merger, tender offer or other business combination involving the Company that is not supported by the Board.

A copy of the Rights Agreement has been or will be filed with the Securities and Exchange Commission as an Exhibit to a Registration Statement on Form 8-A or a Current Report on Form 8-K. A copy of the Rights Agreement is available free of charge from the Company. This summary description of the Rights does not purport to be complete and is qualified in its entirety by reference to the Rights Agreement, which is incorporated herein by reference.