A discrete Cayley number neural network model is presented for the first time,whereby a neuron is a 256-state (±1±i±j±k±e±ie±je±ke). Signal-to-noisetheory is used to analyse the stability and the storage capacity. The storage capacity of theCayley model is the same as that of the Hopfield model. This 256-state neural networkcan be applied to recognize the 256-level color or 256-level grey patterns.