The purpose of this paper is to investigate when a storage function is a state function in discrete time. As shown by Trentelman and Willems [Systems Control Lett., 32 (1997), pp. 249-259], [SIAM J. Control Optim., 36 (1998), pp. 1703-1749], every storage function is a state function in continuous time. At first glance, the same claim seems to hold also in discrete time. Contrary to this expectation, this is not true in general. In fact, the discrete time counterpart involves not only some different but also some more difficult issues compared with the continuous time case. This paper addresses these issues exactly and shows that every nonnegative storage function is a state function of a supply rate with a linear time-invariant dynamical system in discrete time.