  Electing a leader is a classical problem in distributed computing system.
Synchronization between processes often requires one process acting as a
coordinator. If an elected leader node fails, the other nodes of the system
need to elect another leader without much wasting of time. The bully algorithm
is a classical approach for electing a leader in a synchronous distributed
computing system, which is used to determine the process with highest priority
number as the coordinator. In this paper, we have discussed the limitations of
Bully algorithm and proposed a simple and efficient method for the Bully
algorithm which reduces the number of messages during the election. Our
analytical simulation shows that, our proposed algorithm is more efficient than
the Bully algorithm with fewer messages passing and fewer stages.
