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Many fast block-matching algorithms (BMAs) reduce computational complexity by screening the number of checking points. Although many fast BMAs reduce computations, sometimes they should endure matching errors in comparison with full-search algorithm (FSA). In this paper, a novel fast BMA for constrained one-bit transform (C1BT)-based motion estimation is proposed in order to decrease the calculations of the block distortion measure. Unlike the classical fast BMAs, the proposed algorithm shows a new approach to reduce computations. It utilizes the binomial distribution based on the characteristic of binary plane which is composed of only two elements: 0 and 1. Experimental results show that the proposed algorithm keeps its peak signal-to-noise ratio (PSNR) performance very close to the FSA-C1BT while the computational complexity is reduced considerably.