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In this paper, we propose anenergy-aware algorithm to construct a routing backbonein wireless sensor networks. The proposed algorithm selects the backbone members based on the remaining energy of nodes. The node with higher remaining energy will be selected and become the backbone member to relay the message to the sink. The proposed algorithm uses the countdown mechanism; each node checks if it is a backbone member or not only basing on the local information of the node. Therefore, the proposed algorithm does not have the discovery phase. At the end, the simulation result also shows that the proposed algorithm can efficiently reduce the power consumption for constructing the backbone.