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By employing coincidence degree theory and using Halanay-type inequality technique, a sufficient condition is given to guarantee the existence and global exponential stability of periodic solutions for the two-dimensional discrete-time Cohen-Grossberg BAM neural networks. Compared with the results in existing papers, in our result on the exis-tence of periodic solution, the boundedness conditions on the activation are replaced with global Lipschitz conditions. In our result on the exis-tence and global exponential stability of periodic solution, the assump-tions in existing papers that the value of activation functions at zero is zero are removed.