An important challenge in distributed systems is the adoption of suitable and efficient algorithms for coordinator election. The main role of an elected coordinator is to manage the use of a shared resource in an optimal manner. Among all the algorithms the Bully and Ring algorithms have gained more popularity for coordinator election. Leader election is an important problem in distributed computing systems. In this problem, when the leader is crashed, other nodes must elect another leader. Garcia-Molina’s Bully Algorithm is a classic solution to cope with this problem. If the leader crash, the alternative takes, care of the leader's responsibilities. Our results revealed that often, after a leader crash, leader alternative elect as a leader and continue to work. In already existing Election algorithm (also known as Bully Algorithm) proposed by Hector Garcia-Monila (1982). In my paper I proposed about what happens if the crashed leader recovers