Abstract: In distributed systems one process or a node is required in such a way that it can act as leader node or a coordinator. Election algorithms are meant for electing process or node that acts as leader node also called as coordinator from among currently alive processes such that at any instance of time there will be single coordinator for all the processes in the system. So, election algorithms are momentous in any distributed system. Bully algorithm is one of the standard approaches for electing the coordinator in distributed systems. In this paper, we have presented a bully algorithm that minimizes the number of messages while electing the new coordinator and when a process recovers from a crashed state in distributed systems and thus reduces the network traffic caused.