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A wireless sensor network (WSN) typically consists of a large number of small-sized devices that have very low computational capability, small amounts of memory and the need to conserve energy as much as possible (most commonly by entering suspended mode for extended periods of time). Previous approaches for WSN time synchronization do not satisfactorily address all of the requirements of WSN environments. Thus, this paper proposes a new fault-tolerant WSN time sychronization algorithm that is extremely fast (when compared to previous algorithms), achieves a guaranteed level of time synchronization for all non-faulty nodes, can accommodate nodes that enter suspended mode and then wake up, utilizes very little communication and computation resources (thereby leaving those resources available for use by other applications), operates in a completely decentralized manner and tolerates up to f faulty nodes. The efficacy of the proposed algorithm is shown using analysis and experimental results.