A Global-Local Mapping Approximation method is presented in this paper for identifying discrete systems using input-output data. The method is based on the idea that any nonlinear system can be represented as a sum of a discrete linear model and unmodeled nonlinearities. Linear system is then perturbed by a nonlinear term which represents the system nonlinearities that are not captured by the linear model. To identify the discrete systems, discrete learning laws are derived using Lyapunov stability analysis. Numerical examples show the successful application of this technique for identification of nonlinear discrete models using data obtained from the simulations.