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This paper is concerned with the global asymptotic stability of a class of reaction-diffusion Cohen-Grossberg neural networks with continuously distributed delays. Under some suitable assumptions and using a matrix decomposition method, we apply the linear matrix inequality (LMI) method to propose some new sufficient stability conditions for the reaction-diffusion Cohen-Grossberg neural networks with continuously distributed delays. The obtained results are easy to check and improve upon the existing stability results. Some remarks are given to show the advantages of the obtained results over the previous results. An example is also given to demonstrate the effectiveness of the obtained results.