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We studied the Minimum Energy Broadcast problem in wireless sensor network that were subjected to hard constraints on available energy and equipped with directional multibeam antennas by formulating and solving the corresponding optimization problem. Multibeam is the combination of two technologies of multi-channel and directional antennas. It was used to save energy further, improve the throughput and reduce the interference in wireless communication. On the basis of BIP algorithm, which was proposed for constructing the energy efficient broadcast tree in infrastructureless wireless networks with omnidirectional antenna, we presented a greedy algorithm for the solution of the optimization problem. We claimed that when computing the least incremental power to decide which node can be added to the intermediate tree, we only needed to consider two possible cases of beam reassignment. The algorithm has the time complexity of O(mn3).