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Randomized scheduling is a well-known scheduling algorithm for wireless sensor networks to prolong network lifetime. In this algorithm, sensor nodes are randomly assigned to multiple working subsets. These subsets alternatively perform the sensing tasks for monitoring a sensor filed. In each subset, only a portion of sensor nodes are active. It is difficult to maintain the full sensing coverage and network connectivity in a sensor field. For the network connectivity problem of the randomized scheduling, it has been discussed. In this paper, we propose a distributed approach for assisting the randomized scheduling to provide the full coverage. To efficiently achieve this goal, the proposed approach is divided into two main stages: field partition and coverage improvement. The handling problems of these two stages can be transferred to two geometry problems: Voronoi polygon construction and circle covering. Simulation results show that the proposed approach can significantly improve the coverage quality of the randomized scheduling.