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The problem ensuring the global exponential stability (GES) of a class of delayed cellular neural networks (CNNs) with time-varying delays is studied. Without assuming the boundedness of the activation functions, by applying the idea of the Lyapunov function, the linear matrix inequality (LMI) techniques, the free-weighting matrix method, and a novel equation, a new sufficient condition for the GES of CNNs with time-varying delays is obtained, which generalizes the previous results in the literature. The criterion is easy to be verified since it takes the form of an LMI. Three numerical examples are given to illustrate the effectiveness and less conservativeness of our proposed method.