IN THIS PAPER WE FIND THE ORDER AND STRUCTURE OF AUTC(G) FOR G = K H BY IMPOSING SOME CONDITIONS ON H AND K. AS A RESULT, WE SHOW THAT IF M IS A NON-NORMAL MAXIMAL SUBGROUP OF A SOLVABLE GROUP G, SUCH THAT ALL central AUTOMORPHISMS OF G FIX COREG(M) POINTWISE, THEN AUTC(G), IS META-ABELIAN.