Abstract: In this paper, we consider the that discrete-time Hopfield bidirectional associative memory(BAM) neural networks as a special Hopfield network model. We present a novel globally asymptotical stability and globally exponential stability analysis of the equilibrium points for discrete-time Hopfield BAM neural networks. A constraint on the connection matrix has been found under which the neural network has a unique and asymptotically stable equilibrium point. Some sufficient conditions for the globally asymptotical stability and globally exponential stability of equilibrium points are derived using the existence of the positive diagonal solutions of the Lyapunov equations. These conditions can be used to design globally asymptotically stable and globally exponentially stable networks. Analysis in this paper extends the previously known stability results.