In energy-limited wireless sensor networks, network clustering and sensor scheduling are two efficient techniques for minimizing node energy consumption and maximizing network coverage lifetime. When integrating the two techniques, the challenges are how to select cluster heads and active nodes. In this paper, we propose a coverage-aware clustering protocol. In the proposed protocol, we define a cost metric that favors those nodes being more energy-redundantly covered as better candidates for cluster heads and select active nodes in a way that tries to emulate the most efficient tessellation for area coverage. Our simulation results show that the network coverage lifetime can be significantly improved compared with an existing protocol.