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This paper considers the stability analysis problem for neural networks with a constant delay. Based on the dividing of the delay, a new Lyapunov functional is constructed, and a novel delay-dependent stability criterion is derived to guarantee the globally asymptotic stability of the neural network. It is established theoretically that the criterion is less conservative than recently reported ones. Expressed in terms of linear matrix inequalities (LMIs), the stability condition can be checked using the numerically efficient Matlab LMI control toolbox. An example is provided to demonstrate the effectiveness and the reduced conservatism of the analysis result.