Distributed mutual exclusion is a fundamental problem which arises in various systems such as grid computing, mobile ad hoc networks (MANETs), and distributed databases. Reducing key metrics like message count per any critical section (CS) and delay between two CS entrances, which is known as synchronization delay, is a great challenge for this problem. Various algorithms use either permission-based or token-based protocols. Token-based algorithms offer better communication costs and synchronization delay. Raymond's and Suzuki-Kasami's algorithms are well-known token-based ones. Raymond's algorithm needs only O(log(2)(N)) messages per CS and Suzuki-Kasami's algorithm needs just one message delivery time between two CS entrances. Nevertheless, both algorithms are weak in the other metric, synchronization delay and message complexity correspondingly. In this work, a new hybrid algorithm is proposed which gains from powerful aspects of both algorithms. Raysuz's algorithm (the proposed algorithm) uses a clustered graph and executes Suzuki-Kasami's algorithm intraclusters and Raymond's algorithm interclusters. This leads to have better message complexity than that of pure Suzuki-Kasami's algorithm and better synchronization delay than that of pure Raymond's algorithm, resulting in an overall efficient DMX algorithm pure algorithm.