Fast algorithms for high-speed divider design in finite fields GF(2m) are very crucial in applications like cryptosystems. In this paper, we reformulated the conventional iterative division algorithm by changing the pre-defined variable and then updating its initial value accordingly. The reformulated division algorithm allows a restructuring of the divider architecture to further improve its operating speed without increasing latency or area cost. Using the proposed fast algorithm, we developed two high-speed iterative dividers based on the semi-systolic and bit-serial systolic architectures. Analytical results show that the cost of the initial value update and variable transformation in the reformulated algorithm is almost negligible in the hardware implementation. Our divider designs improve the critical path delay. Compared with related divider designs, the proposed designs have time and area advantages.