In real-time applications of bi-directional associative memory (BAM) networks, a global exponentially stable equilibrium is highly desired. The existence, uniqueness and global exponential stability for a class of BAM networks are studied in this paper, the signal function of neurons is assumed to be piece-wise linear from the engineering point of view. A very concise condition for the equilibrium of such a network being globally exponentially stable is derived,which makes the practical design of this kind of networks an easy job.