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Compared with traditional terrestrial radio transmissions in Wireless Sensor Networks (WSNs), the challenges of transmissions in UnderWater Sensor Networks (UWSNs) include lower transmission rate, longer delay time, and higher power consumption. In such a circumstance, the negative effects of transmission collisions deteriorate. Most of the existing UWSN MAC protocols handle the collision problem in a single hop or light-loaded environment. They fail to function effectively in a multi-hop network consisting of more sensor nodes with heavier traffic loads. In this paper, using the concept of cyclic quorum systems, we propose a distributed multiple rendezvous multichannel MAC protocol, MM-MAC, to reduce collision probability. The advantages of the proposed protocol are threefold: 1) Only one modem is needed for each node to solve the missing receiver problem which is often encountered in multichannel protocols. 2) Multiple sensor node pairs can complete their channel negotiations on different channels simultaneously. 3) Data packets will not be collided by control packets, and vice versa. Simulation results verify that our protocol can reduce collision probability significantly which enhances the network performance in a multi-hop UWSN.