In this paper, we propose a motion estimation algorithm for the discontinuity blocks. The algorithm uses sub-SAD value (i.e. the sum of absolute difference for a quarter of a block) to identify the discontinuity region, and produces additional motion vectors for these sub-blocks if necessary. We show with experimental results that, in comparison with some conventional motion estimation algorithms, the proposed algorithm achieves quality enhancement for the sequences with discontinuity blocks, and also shows the same computational quantity as to normal algorithms for sequences with less discontinuity.