Understanding the synchronization process of self-propelled objects is of great interest in science and technology. We propose a synchronization model for a self-propelled objects system in which we restrict the maximal angle change of each object to θR. At each time step, each object moves and changes its direction according to the average direction of all of its neighbors (including itself). If the angle change is greater than a cutoff angle θR, the change is replaced by θR. We find that (i) counterintuitively, the synchronization improves significantly when θR decreases, (ii) there exists a critical restricted angle θRc at which the synchronization order parameter changes from a large value to a small value, and (iii) for each noise amplitude η, the synchronization as a function of θR shows a maximum value, indicating the existence of an optimal θR that yields the best synchronization for every η.