In this paper, we propose a new multichannel allocation protocol for ZigBee/IEEE 802.15.4 networks. The main goal is to improve the global throughput which is basically insufficient to satisfy high bandwidth requirements for applications like monitoring or traffic control. The solution is based on the availability of multiple channels on current low- cost, low-energy radio transceivers, such as TI/Chipcon CC2420, which can be easily tuned dynamically to different frequencies. This possibility can be exploited to increase the number of simultaneous transmissions on adjacent links. The allocation of the different channels is centralized and distributed by the coordinator thanks to a function designed to compute the channel offset between two successive children routers. In the nodes, the switching process between the transmission and the reception channels is triggered starting from the PHY primitive available on the transceiver. The evaluation shows that the proposed protocol improves the global throughput by a factor between 2 and 5, depending on the scenario, compared to the single-channel solution or a random channel allocation.