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In this paper, two faster algorithms - fast predictive search algorithm (FPSA) and fast predictive search algorithm-early termination (FPSA-ET), used in motion estimation were proposed. These algorithms are proceeded by the temporal and spatial correlation between BMA and the film and by the prediction of motor vectors. The video coding is generally following the order from top to down and left to right and it causes the spatial correlation between the adjacent blocks, especially for those blocks on the left and up sides. The motion of the object in the image would follow the constant trace, so there would be temporal correlation between the blocks. Based on the experimental data of this paper, the proposed algorithms are faster than the conventional one for about 20%~25% and faster than UMHexagonS for about 20 times. The PSNR value of the proposed algorithms are higher than the conventional one for 0.22dM~0.32dM. Therefore the proposed algorithms are more appropriate for the real-time or high quality video or for video with large amounts of motion.