We propose MCCT (Multi-Channel Cluster Tree), a cluster-tree construction protocol for nodes in IEEE 802.15.4 beacon-enabled mode. By multiplexing transmissions across orthogonal channels, we reduce collisions between control and data frames, which leads to better packet delivery rate and fairness. We propose a method for constructing a cluster-tree suitable for minimizing beacon collisions. The protocol builds on a neighbor discovery procedure that uses a dedicated control channel while still sticking to the superframe structure of IEEE 802.15.4. We also specify a channel assignment and superframe scheduling method that takes into account channel diversity. We evaluate the proposed protocol through simulation and compare with other proposals: standard 802.15.4 and a representative of distributed solutions to the superframe scheduling problem - MeshMAC. The simulation results show that MCCT significantly improves packet delivery ratio, delay, and fairness. It also results in very good packet delivery ratio for increased network density.