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In this paper, we design a destination-driven on-demand multicast routing protocol for wireless ad hoc networks. The design objective is to improve the multicast forwarding efficiency. To achieve this goal, the path to reach a multicast destination is biased towards those paths passing through another multicast destination. If multiple such choices are available, the one leading to the least extra cost is selected. Our protocol embeds this destination-driven feature into the on-demand multicast structure building process of an existing multicast protocol ODMRP. Detailed protocol design descriptions are provided. Simulation results show that our protocol can greatly improve the forwarding efficiency as compared with ODMRP. Moreover, our destination-driven design can also work well with other existing multicast routing protocols for wireless ad hoc networks.