To implement elliptic curve cryptosystem in $GF(2^m)$ at high speed, a fast divider is required. This paper a divide algorithm for computing modular division A(x)/B(x) mod G(x) in finite fields $GF(2^m)$. Based on the binary GCD(Greatest Common Divisor) algorithm and a modified version of the binary extended GCD algorithm, we design a new divide algorithm over finite field $GF(2^m)$. Furthermore, since this proposed algorithm does not restrict the choice of irreducible polynomial, and has a unidirectional data flow and has regularity and modularity, it provides a high flexibility and scalability with respect to the field size n Therefore, the proposed divide algorithm is well suited to the FPGA implementation.