Summary: A new bidirectional associative memory is presented. Unlike many existing BAM algorithms, the presented BAM uses an optimal associative memory matrix in place of the standard Hebbian or quasi-correlation matrix. The optimal associative memory matrix is determined by using only simple correlation learning, requiring no pseudoinverse calculation. Guaranteed recall of all training pairs is ensured by the present BAM. The designs of a linear BAM (LBAM) and a nonlinear BAM (NBAM) are given, and the stability and other performances of the BAMs are analyzed. The introduction of a nonlinear characteristic enhances considerably the ability of the BAM to suppress the noises occurring in the output pattern, and reduces largely the spurious memories, and therefore improves greatly the recall performance of the BAM. Due to the nonsymmetry of the connection matrix of the network, the capacities of the present BAMs are far higher than that of the existing BAMs. Excellent performances of the present BAMs are shown by simulation results.