Montgomery modular multiplication algorithm is commonly used in implementations of the RSA cryptosystem and other cryptosystems with modular operations. Radix-2 version of this algorithm is simple and fast in hardware implementations. In this paper this algorithm is modified with a new recoding method to make it simpler and faster. We have also implemented this new algorithm with carry save adders. Results show that, in average the proposed algorithm has about 47% increase of data throughput with maximum 7% increase of hardware area comparing with conventional algorithm.