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Previous quality-of-service (QoS) routing/multicasting protocols in mobile ad hoc networks determined bandwidth-satisfied routes for QoS applications. However, they suffer from two bandwidth-violation problems, namely, the hidden route problem (HRP) and the hidden multicast route problem (HMRP). HRP may arise when a new flow is permitted and only the bandwidth consumption of the hosts in the neighborhood of the route is computed. Similarly, HMRP may arise when multiple flows are permitted concurrently. Not considering the bandwidth consumption of two-hop neighbors is the reason that the two problems are introduced. In this paper, a novel algorithm that can avoid the two problems is proposed to construct bandwidth-satisfied multicast trees for QoS applications. Furthermore, it also aims at minimizing the number of forwarders so as to reduce bandwidth and power consumption. Simulation results show that the proposed algorithm can improve the network throughput.