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This paper studies the problem of stability analysis for neural networks (NNs) with a time-varying delay. Unlike the previous works, the activation functions are assumed to be neither monotonic, nor differentiable, nor bounded. By defining a more general type of Lyapunov functionals, some new less conservative delay-dependent stability criteria are established in terms of linear matrix inequalities (LMIs). Meanwhile, the computational complexity of the newly obtained stability conditions is reduced because less variables are involved. Numerical examples are given to illustrate the effectiveness and the benefits of the proposed method.