In this paper, a method is proposed to design a periodic output feedback controller for discrete two-time scale system. Using explicitly invertible transformation the two-time scale system is converted into the decoupled form which gives a slow subsystem and a fast subsystem. Then by using two stage feedback design a composite controller is designed which provides output injection gain. This output injection gain has been used to compute the periodic output feedback gain. The method does not require the states of the system for feedback. The method is illustrated by numerical examples.