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We envisage extending the coverage of existing terrestrial wireless broadband wireless networks to the sea so that cost-efficient wireless access is available to the ships near the shore. The coverage extension is achieved through a multi-hop WiMAX wireless mesh networks where ships, maritime beacons and buoys are the nodes. In such a multi-hop network, routing protocol plays an important role in ensuring reliable end-to-end packet delivery. Compared to AOMDV and OLSR, AODV has been found as a more suitable routing protocol in terms of average packet delay, packet delivery ratio, and implementation complexity. AODV requires route request messages being broadcast during route discovery process. However, WiMAX mesh MAC protocol is not efficient in supporting broadcast of data packets that carry the route request. This inefficiency is due to need of performing the three-way-handshaking process in reserving a data slot before transmitting each route request. As a result, AODV suffers from large initial packet delay and average packet delay. In view of the problem, this paper proposes a method to efficiently deliver the AODV routing messages by piggybacking them on the existing WiMAX mesh MAC control messages. As such, the three-way-handshaking is avoided leading to a faster transmission of routing messages. Simulation results confirm that the proposed scheme can lead to an improvement in initial packet delay, weighted average delay, and packet delivery ratio.