Many of software in distributed systems require a special process called the coordinator or the leader. The coordinator is elected among the processes participating a particular distributed service when the service begins operation or the existing coordinator fails. The procedure of selecting the coordinator is called the election. One of the most popular election algorithms is the bully algorithm. However, this algorithm is costly because it generates O(n2) messages for n processes. Also the time delay till the completion of the election is considerably long. This paper proposes a new election algorithm called the fast bully algorithm. The algorithm is described and performance of the algorithm has been analyzed. The fast bully algorithm shows a clear performance improvement. It works with less messages, only O(n) messages, and with shorter time delay than the bully algorithm. Also the problem of having two coordinators at the same time that appears by the bully algorithm can be avoid