Based on the real world image sequence's characteristic of center-biased motion vector distribution, a new four-step search (JSS) algorithm with center-biased checking point pattern for fast block motion estimation is proposed in this paper. Halfway-stop technique is employed in the new algorithm with searching steps of 2 to 4 and the total number of checking points is varied from 17 to 27. Simulation results show that the proposed 4SS performs better than the well-known three-step search and has similar performance to the new three-step search (N3SS) in terms of motion compensation errors. In addition, the 4SS also reduces the worst-case computational requirement from 33 to 27 search points and the average computational requirement from 21 to 19 search points as compared with N3SS.