Utilization of multiple channels in ad hoc networks provides the benefits of reducing the probability of collisions, decreasing the normalized propagation delay and support of QoS. However, problems like busy waiting or deadlock existence degrade the bandwidth utilization. In this paper, we present the modelling of the transmission-request network as a directed graph in the multi-channel environment. A distributed self-stabilizing algorithm which performs maximal matching is also presented for the new model. By using the algorithm, we propose a new multi-channel MAC protocol, named MAXM (MAXimal Matching multi-channel MAC protocol), for ad hoc networks. The idea of MAXM is to maximize utilization of bandwidth by adopting maximal matching. MAXM is deadlock-free, self-stabilizing and able to converge in finite time. Simulation results show that MAXM offers significant improvements over previous work in throughput and transmission delay.