We incorporate the early zero-block detection technique into the UMHexagonS algorithm, which has already been adopted in H.264/AVC JM reference software, to speed up the motion estimation process. A nearly sufficient condition is derived for early zero-block detection. Although the conventional early zero-block detection method can achieve significant improvement in computation reduction, the PSNR loss, to whatever extent, is not negligible especially for high quantization parameter (QP) or low bit-rate coding. This paper modifies the UMHexagonS algorithm with the early zero-block detection technique to improve its coding performance. The experimental results reveal that the improved UMHexagonS algorithm greatly reduces computation while maintaining very high coding efficiency.