In this paper, we reformulated the conventional iterative division algorithm by substituting 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 and area cost. Using the proposed fast algorithm, we developed a high-speed bit-serial GF(2m) divider. 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 reduces the critical path delay. Compared with related divider designs, the proposed design has time and area advantages.