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This paper proposes a novel discrete time second- order distributed consensus time synchronization (SO-DCTS) algorithm for wireless sensor networks. The consensus properties and convergence rates of the SO-DCTS algorithm are analyzed for both directed and undirected networks. Additionally, the convergence region and optimal convergence rate of the SO- DCTS algorithm are determined for undirected networks and this convergence rate is shown to be superior to that of the first-order DCTS (FO-DCTS) algorithm under careful algorithm design. Finally, simulation results are provided to verify these analytical results.