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This paper deals with the initial shift problem that arises from discrete-time iterative learning control. A unified learning scheme is considered for a class of nonlinear systems with well-defined relative degree, which adopts the error data with anticipation in time and provides wider freedom for the updating law formation. The sufficient convergence condition is derived to enable the system to possess asymptotic tracking capability and the converged output trajectory can be assessed by the initial condition. The tracking performance is improved further by the introduction of initial rectifying action and the complete tracking is achieved over a specified interval.