We consider d(K, L) a modified version of the Banach-Mazur distance of convex bodies in Rn proposed by Grünbaum. Gordon, Litvak, Meyer and Pajor in 2004 showed that for any two convex bodies d(K, L) = n, moreover, if K is a simplex and L=-L then d(K, L)=n. The following question arises naturally: Is equality only attained when one of the sets is a simplex? Leichtweiss, and later Palmon proved that if d(K, B2n)=n, where B2n is the Euclidean ball, then K is the simplex. We prove the affirmative answer to the question in the case when one of the bodies is strictly convex or smooth, thus obtaining a generalization of the result of Leichtweiss and Palmon.