In this paper, we proposed computationally efficient filter structures based on the frequency response masking (FRM) technique for the synthesis of arbitrary bandwidth sharp FIR filters. A two-step masking approach is introduced in the new structures to further reduce the arithmetic operations in the overall filter compared to original FRM structure. It was shown, by means of examples, that additional 12% to 17% savings in terms of numbers of arithmetic operations are achievable for the new structures.