The paper presents an approach to the statistical linearization of the input/output mapping of a non-linear discrete-time stochastic system driven by a white-noise Gaussian process. The approach is based on applying the maximal correlation function. At that, the statistical linearization criterion is the condition of coincidence of the mathematical expectations of the output processes of the system and model, and the condition of coincidence of the joint maximal correlation functions of the output and input processes of the system and the output and input processes of the model. Explicit expressions for the weight function coefficients of the linearized model are obtained.