An algebraic Riccati equation (ARE) approach to the reduced-order H-infinity controller design problem is proposed. It is shown that the order of H-infinity controller can be reduced to r, where r is the rank of the stabilizing solution W-infinity to an ARE in W developed in Petersen, Anderson and Jonckheere (1991, International Journal of Robust Nonlinear Control, 1, 171-185). State-space formulas for the reduced-order H-infinity controller design are also given in terms of the stabilizing solutions to the two standard H-infinity AREs. The development uses only elementarily algebraic ideas, mainly the bounded real lemma, thus the proofs given are simple and clear.