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We propose a new approach for analyzing the global asymptotic stability of the extended discrete-time bidirectional associative memory (BAM) neural networks. By using the Euler rule, we discretize the continuous-time BAM neural networks as the extended discrete-time BAM neural networks with non-threshold activation functions. Here we present some conditions under which the neural networks have unique equilibrium points. To judge the global asymptotic stability of the equilibrium points, we introduce a new neural network model — standard neural network model (SNNM). For the SNNMs, we derive the sufficient conditions for the global asymptotic stability of the equilibrium points, which are formulated as some linear matrix inequalities (LMIs). We transform the discrete-time BAM into the SNNM and apply the general result about the SNNM to the determination of global asymptotic stability of the discrete-time BAM. The approach proposed extends the known stability results, has lower conservativeness, can be verified easily, and can also be applied to other forms of recurrent neural networks.