The dynamics of discrete neural network with delay are studied in this paper using a matrix inequality which is shown to be equivalent to the state transition equation of the network. For the network with arbitrary weight matrix, the conditions for the existence of cycle of length 1 and 2 are presented. Also, the conditions for the existence of special cycle of length 1, 2 and 4, for having no any stable states are achieved. Computer simulations demonstrate that the theoretical analysis is correct.