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The IEEE 802.15.4 protocol offers great potential for industrial wireless sensor networks, especially when operating in beacon-enabled mode over star or cluster-tree topologies. However, it is known that beacon collisions can undermine the reliability of cluster-tree networks, causing loss of synchronization between nodes and their coordinator. For this reason, this paper proposes a Multichannel Superframe Scheduling (MSS) algorithm, a novel technique that avoids beacon collisions by scheduling superframes over different radio channels, while maintaining the connectivity of all the clusters. The paper describes the MSS algorithm and addresses the advantages it provides over the time-division superframe scheduling. Analytical results are shown which provide a quantitative estimation of how the schedulability space is improved, while simulation results show that the proposed technique increases the number of schedulable clusters and the maximum cluster density. Finally, this paper proves the feasibility of the proposed approach describing a working implementation based on TinyOS.