The design of a state feedback controller for a class of SISO non-linear discrete-time systems is proposed. Namely, an alternative adaptive scheme is stated for the parametric-strict-feedback form. The control objective is to achieve tracking of a reference signal. Backstepping control is combined with a parameter estimator based on an orthogonalization process which overcomes the drawback of over-parameterization. Without assuming any growth conditions on the non-linearities, global boundedness and convergence are obtained in the closed loop system.