The challenge in the deployment of wireless sensor networks is to ensure the coverage of targets with high energy efficiency, particularly when coverage constraint and energy constraint must be taken into account. Many algorithms have been suggested over the years to enhance network lifetime as sensor nodes are powered by batteries. These algorithms divide a set of sensor nodes into a number of subsets which can monitor all targets. The subsets are either joint or disjoint. In this paper, we propose an efficient method to compute the maximum lifetime target coverage. Our proposed method is centered around a target that is covered by a minimum number of sensor nodes. Based on this approach, we also propose an algorithm to expand the network lifetime which guarantees the monitoring of all targets by forming subsets of sensor nodes. Our obtained results are compared with the work reported in [1]. They are also compared with a method of computing the maximum lifetime target coverage (MLTC). The results obtained by simulation show that the proposed algorithm enhances the network lifetime, which illustrates the efficiency of this algorithm.