The design of an H-infinity multistep predictor aims at constructing an estimator which guarantees a prescribed level of energy attenuation from the disturbances to the prediction error. For a given value of the attenuation, an admissible predictor exists only if the solution of a suitable difference Riccati equation satisfies a certain matrix inequality (feasibility condition). The purpose of this paper is to determine a set of initial conditions of the Riccati equation for which the feasibility of the solution is guaranteed over an arbitrarily long time interval. Convergence of the predictor to a stationary one is also discussed.