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Mutual Exclusion is one of the most studied topics in distributed systems where processes communicate by asynchronous message passing. It is often necessary for multiple processes at different sites to access a shared resource or data called a critical section (CS) in distributed systems. A number of algorithms have been proposed to solve the mutual exclusion problem in distributed systems. In this paper, we propose the new algorithm which is modified from Garg's algorithm[1] thus works properly in a fault-tolerant system. In our algorithm, after electing the token generator, the elected process generates a new token based on the information of the myreqlist which is kept by every process and the reqdone which is received during election. Consequently, proposed algorithm tolerates any number of process failures and also does even when only one process is alive.