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