A square matrix A with $per A eq 0$ is called convertible if there exists a {1, -1} matrix H such that $per A = det(H circ A)$ where $H circ A$ denote the Hadamard product of H and A. In this paper, ranks of convertible {0, 1} matrices are investigated and the existence of maximal convertible matrices with its rank r for each integer r with $leftlceil frac{n}{2} ight ceil leq r leq n$ is proved.