In this paper the standard discrete-time H-infinity control problem is considered under the constraint imposed upon the controller to be strictly proper. The necessary and sufficient conditions for the existence of a gamma-suboptimal controller are derived and the set of all linear time-invariant controllers, which solve the problem, is parametrized. In contrast with the unconstrained case, the state-space solution obtained is very transparent and actually is not more complex than the solution of the continuous-time H-infinity problem.