This note investigates the problem of output feedback H-infinity control for linear discrete-time systems. Three types of H-infinity controllers are considered, namely, static output feedback controllers, dynamic output feedback controllers, and observer-based output feedback controllers. New design conditions for the three type of output feedback controllers are introduced in terms of unified linear matrix inequality (LMI) representations, which guarantee the prescribed H-infinity performances of the closed-loop systems. In contrast to the existing H-infinity conditions for designing the output feedback H-infinity controllers, the improvement of the proposed results over the existing ones is shown by theoretical proof and numerical example.