In this paper, a new improved exponential bidirectional associative memory (IeBAM) model is proposed. Its stability in synchronous and asynchronous updating modes of the states is proven by defining an energy function which is bounded and decreases as the states change. On one hand, IeBAM eliminates the unreasonable hypotheses in the stability proofs of both Wang's modified exponential BAM (MeBAM) and Jeng's exponential BAM (eBAM). On the other hand, it relaxes the continuity assumption of the BAM (bidirectional associative memory) and avoids the complement encoding problem. The theoretical analysis and computer simulations indicate that the IeBAM has higher storage capacity and better error-correcting capability than the MeBAM and the eBAM.