The damping ratio ${xi}$ of the unit-step response of a second-order discrete system is a function of only the location of the closed-loop poles and is not directly related to the location of the system zero. However, the peak overshoot of the response is the function of both the damping ratio ${xi}$ and an angle ${alpha}$, which is the phasor angle of the damped sinusoidal response and is determined by the relative location of the zero with respect to the closed-loop poles. Therefore, if the zero and the open-loop poles are relatively adjusted, through pole-zero cancellation, to maintain the desired (or designed) closed-loop poles, the damping ratio ${xi}$ will also be maintained, while the angle ${alpha}$ changes. Accordingly, when the closed-loop system poles are fixed, the peak overshoot is considered as a function of the angle ${alpha}$ or the system zero location. In this paper the effects of the relative location of the zero on the system performance of a second-order discrete system is studied, and a design method of digital compensator which achieves a minimum peak overshoot while maintaining the desired system mode and the damping ratio of the unit step response is presented.