[attachment=449]Many algorithms for achieving mutual exclusion in distributed computing systems have been proposed. The three most often used performance measures are the number of messages exchanged between the nodes per Critical Section (CS) execution, the response time, and the synchronization delay. In this paper, we present a new fully distributed mutual exclusion algorithm. A node requesting the CS sends out the request message which will roam in the network. The message will be forwarded among the nodes until the requesting node obtains enough permissions to decide its order to enter the CS. The decision is made by using Relative Consensus Voting (RCV), which is a variation of the well-known Majority Consensus Voting (MCV) scheme. Unlike existing algorithms which determine the node to enter the CS one by one, in our algorithm, several nodes can be decided and ordered for executing the CS. The synchronization delay is minimal. Although the message complexity can be up to O(N) in the worst case in a system with N nodes, our simulation results show that, on average, the algorithm needs less number of messages and has less response time than most of those existing algorithms which do not require a logical topology imposed on the nodes. This is especially true when the system is under heavy demand. Another feature of the proposed algorithm is that it does not require the FIFO property of the underlying message passing mechanism