In this paper, we present a simple and efficient distributed mutual exclusion algorithm for a distributed computer system of N geographically dispersed autonomous computer sites which communicate with each other only by sending messages and do not share any memory. The intent of this work is to extend a previously known mutual exclusion algorithm given by Lamport (1978) from one entry to critical selection 2D a multiple entries to critical section. Some of the proposed multiple entries algorithms have prolonged the response time and synchronization delay when they have extended the one entry to critical section algorithm to multiple entries to the critical section algorithm with the same number of message traffic. Here we present an algorithm which reduces the message traffic while it maintains the same response time and synchronization delay. The algorithm is deadlock free and free from starvation. Comparing it with Raymond's algorithm (1989), our algorithm can save 25% of messages in the best case.