Abstract: The correlated network of a Hopfield network is defined and the properties of correlated networks are analyzed. The relationship between the state transferences of any two correlated networks on the correlating law is found out, with which the state transference of a Hopfield network can be easily deduced by that of any network correlated with it. The relationship between the attractors of any two correlated networks is derived out, which is helpful for the Hopield network to escape from the local minimum and for the judgement of network's tolerant ability to input data. Finally, computer simulation results are presented to verify the existance of the correlating law.