In this paper, the steady-state behaviour of discretized terminal sliding mode control is studied. A discrete terminal sliding mode control is designed by discretizing the continuous-time system and then the steady-state behaviour is analysed in terms of periodic orbits. We have shown that by this discrete terminal sliding mode control the discretized second order system exhibits only period-2 motion in steady-state. To ensure this, existence and stability conditions of all possible periodic orbits are found out analytically and shown that only period-2 conditions are satisfied by the state evolution of the discretized system in steady-state. Next, a higher order single-input-single-output system is considered and we also establish that only period-2 motion exists in steady-state.