Based on Kosko’s bidirectional associative memory（BAM） and Kohonen’s generalized inverse associative memory（GIAM）

we propose a constrained least square bidirectional associative memory（CLSBAM）whose associative matrix（or connection weight matrix）satisfies a famous Lyapunov matrix equation.Unlike BAM

CLSBAM can handle not only dual polar data but also real number

and unlike GIAM

it possesses bidirectional and optimal assocative function under some constraints.Finally

with matrix singular value decomposition（SVD） theory and computer simulation

the feasibility of CLSBAM is confirmed.