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In centralized algorithm for mutual exclusion, one process is elected as a coordinator. Whenever a process wants to go to critical section, it sends a request message to the coordinator and asks for permission. The election of coordinator is an important problem in distributed systems. After a failure occurs in the system, it is necessary to reelect a new leader as a coordinator. The bully election algorithm is one of the classic methods which is used to determine the process with highest priority number as the coordinator. But this algorithm often needs a lot of message passing to find out which process should be a new coordinator. In this paper we are going to propose an optimized method for the bully algorithm called modified bully algorithm. Our analytical simulation shows that, our algorithm has fewer message passing and is more efficient.