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This paper discusses the global output convergence of a class of continuous-time recurrent neural networks (RNNs) with globally Lipschitz continuous and monotone nondecreasing activation functions and locally Lipschitz continuous time-varying thresholds. We establish one sufficient condition to guarantee the global output convergence of this class of neural networks. The present result does not require symmetry in the connection weight matrix. The convergence result is useful in the design of recurrent neural networks with time-varying thresholds.