Exhibit 4

                         FIRST AMENDMENT TO RIGHTS AGREEMENT

     This FIRST AMENDMENT TO RIGHTS AGREEMENT is made and entered into as of
the 27th day of May 1999 by and between Armco Inc., an Ohio corporation (the
"Company"), and Fifth Third Bank (the "Rights Agent").

                         W I T N E S S E T H
                         - - - - - - - - - -

     WHEREAS, the Company and the Rights Agent entered into a Rights Agreement
dated as of February 23, 1996 (the "Rights Agreement");

     WHEREAS, the Company has entered into an Agreement and Plan of Merger
dated as of May 20, 1999 with AK Steel Holding Corporation and AK Steel
Corporation (the "Merger Agreement"), pursuant to which the Company shall be
merged with and into AK Steel Corporation, which shall be the surviving
corporation;

     WHEREAS, it is a requirement under the Merger Agreement that the Board of
Directors of the Company take all necessary action so that (a) neither the
execution or delivery of the Merger Agreement, nor the actions contemplated
thereby, cause (i) the rights issued pursuant to the Rights Agreement to
become exercisable under the Company Rights Agreement or a Distribution Date
(as defined in the Rights Agreement), (ii) AK Steel Holding Corporation or AK
Steel Corporation to be deemed an Acquiring Person (as defined in the Rights
Agreement), or (iii) the Distribution Date (as defined in the Company Rights
Agreement) to occur upon any such event; and (b) the Expiration Date (as
defined in the Rights Agreement) of the rights shall occur immediately prior
to the consummation of the merger under the Merger Agreement.

     NOW, THEREFORE, in consideration of the agreements contained herein, and
for other good and valuable consideration, the receipt and sufficiency of
which are hereby acknowledged, and intending to be legally bound hereby, the
parties hereto agree as follows:

     1.  The recitals set forth hereinabove are incorporated by reference with
the same force and effect as if fully set forth herein;

     2.  The Rights Agreement shall be amended as set forth below:

         (a)   The definition of "Acquiring Person" in Section 1(d) is hereby
amended by adding the following proviso the end of such section:

      provided, however, that the definition of "Acquiring Person" shall not
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 include either AK Steel Holding Corporation ("AK Holding") or AK Steel
Corporation ("AK Corp."), so long as both companies consummate the
transactions contemplated by, and consistent with the terms provided under,
the Agreement and Plan of Merger dated as of May 20, 1999 among the Company,
AK Holding and AK Corp. (as it may be amended in accordance with its terms
with the approval of the Board of Directors of the Company) on or before March
31, 2000.

 

      (b)  Section 7(a) shall be amended in its entirety such that it shall
read in its entirety as follows:

            (a)  Subject to Section 7(e) hereof, the registered holder of any
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 Rights Certificate may exercise the Rights evidenced thereby (except as
otherwise provided herein, including, without limitation, the restrictions on
exercisability set forth in Section 9(c), Section 11(a)(iii) and Section 23(a)
hereof) in whole or in part at any time after the Distribution Date upon
surrender of the Rights Certificate, with the form of election to purchase and
the certificate on the reverse side thereof duly executed, to the Rights Agent
at the office of the Rights Agent designated for such purpose, together with
payment of the aggregate Purchase Price with respect to the total number of
one two-hundredths of a share of Preferred Stock (or other securities, cash or
other assets, as the case may be) as to which such surrendered Rights are then
exercisable, at or prior to the earliest of (i) the Final Expiration Date,
(ii) the time at which the Rights are redeemed as provided in Section 23
hereof and (iii) the time that is immediately prior to the Effective Time as
such term is defined in the Agreement and Plan of Merger dated as of May 20,
1999 among the Company, AK Steel Holding Corporation and AK Steel Corporation
(the earliest of (i), (ii) and (iii) being herein referred to as the
"Expiration Date").

     3.  Except as amended hereby, the Rights Agreement shall remain in full
force and effect in accordance with the provisions thereof.

     4.  This Amendment may be executed in counterparts, each of which shall
be an original but which together shall constitute one instrument

     IN WITNESS WHEREOF, the undersigned have executed this First Amendment to
Rights Agreement as of the day and year first hereinabove written.

                                       ARMCO INC.

                                       By:  /s/  Jerry W. Albright
                                          ------------------------
                                       Name:  Jerry W. Albright
                                       Title: Vice President

                                       FIFTH THIRD BANK


                                       By:  /s/ Dana S. Hushak
                                         --------------------------
                                       Name:  Dana S. Hushak
                                       Title: Vice President