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This brief deals with the stability analysis problem for recurrent neural networks with delay. An improved stability condition is derived to guarantee the existence of the unique equilibrium point and its globally exponential stability, which is shown with novel methods. Both delay-dependent and delay-independent stability conditions are obtained. Expressed in terms of LMIs, they can be checked using the numerically efficient Matlab LMI toolbox. Examples are provided to demonstrate the effectiveness and the reduced conservatism of the analysis results.