This paper addresses the existence and design methods of reduced-order controllers for the H-infinity control problem with unstable invariant zeros in the state-space realization of the transfer function matrix from the control input to the controlled error or from the exogenous input to the observation output, where the realization is induced from a stabilizable and detectable realization of the generalized plant. This paper presents a new controller degree bound for the H-infinity control problem in terms of the minimal rank of the system matrix pencils of these two transfer function matrices in the unstable region. When the unstable invariant zero exists, this paper shows that reduced-order controllers with orders strictly less than that of the generalized plant exist if the H-infinity control problem is solvable. Moreover, this paper shows that the computational problem of finding the controllers with the new degree bound is convex by providing two linear matrix inequality-based design methods (algorithms) for constructing the reduced-order controllers. The results developed in this paper are valid both for the continuous- and discrete-time H-infinity control problems. (C) 2003 Elsevier Ltd. All rights reserved.