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Directional sensor networks (DSNs) comprise a large number of sensors equipped with a limited battery and limited angles of sensing range. In DSNs, maximizing network lifetime while covering all the targets in a given area is still a challenge problem. A major technique to save the energy power of sensors is to use a node wake-up scheduling protocol by which some sensor nodes stay active to provide sensing service, while the others are inactive for conserving their energy. In this paper, we first address the MSCD (Maximum Set Cover for DSNs) problem that is known as NP-complete and then present a new target coverage scheduling scheme to solve this problem with a greedy algorithm. To verify and evaluate the proposed scheme, we conduct simulations and show that it can contribute to extending the network lifetime largely. By the simulations, we also present an energy-efficient strategy to choose a sensor in order to organize a scheduling set in the greedy scheme.