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This paper addresses the maximal lifetime scheduling problem in sensor surveillance networks. Given a set of sensors and targets in a Euclidean plane, a sensor can watch only one target at a time, our task is to schedule sensors to watch targets, such that the lifetime of the surveillance system is maximized, where the lifetime is the duration that all targets are watched. We propose an optimal solution to find the target watching schedule for sensors that achieves the maximal lifetime. Our solution consists of three steps: 1) computing the maximal lifetime of the surveillance system and a workload matrix by using linear programming techniques; 2) decomposing the workload matrix into a sequence of schedule matrices that can achieve the maximal lifetime; 3) obtaining a target watching timetable for each sensor based on the schedule matrices. Simulations have been conducted to study the complexity of our proposed method and to compare with the performance of a greedy method.