This paper presents a proof of a connection between the strong solutions to three algebraic Riccati equations which are associated with the solution of a discrete-timeH∞-optimal control problem. Of these solutions, denoted X∞, Y∞" and Z∞, two parametrize a generator of all γ-suboptimal output-feedback controllers and one is associated with a dual state-feedback problem. The relationship is proved by establishing the existence of a similarity transformation between two symplectic matrix pencils which are associated with two of the Riccati equations. A similar result is known to exist in the continuous-time setting.