Summary: The present paper presents a new technique for designing associative memories to be implemented by Hopfield neural networks. This technique guarantees that each desired memory is stored and is attractive. The procedure also guarantees that the resulting network is implementable, a requirement often overlooked by other methods. The present synthesis procedure does not require a symmetric interconnection matrix; instead, stability is guaranteed by use of the results presented in [A. N. Michel, J. A. Farrell, W. Porod
, IEEE Trans. Circuits Syst. CAS-36, No.2, 229-243 (1989; Zbl 0672.94015
)]. Two examples are presented that demonstrate the synthesis procedure’s storage ability and flexibility.