Let R = (r 1 , r 2 ,...,r m ) and S = (s 1 , s 2 ,...,s n ) be two positive integral vectors with Σ m i = 1 r i = Σ n j = 1 s j = N 1 . Denote by U(R, S) the class of all m x n (0, 1)-matrices having row sum vector R and column sum vector S. The interchange graph G(R, S) is the graph where the vertices are the matrices in U(R, S) and two vertices are adjacent provided they differ by an interchange. We prove that the diameter of interchange graph is less than N 1 -(m/2) ln[(mn+2m)/(mn-2N 1 +4m)]. As a corollary of this result, we lower the upper bound (mn/2) - 1 obtained by Brualdi to (mn/2) - (m/2) ln[(n + 2)/4], which depends only on the size m and size n.