We establish conjugation notion in discrete-time systems, first introduced into theH∞control theory of continuous-time systems by Kimura (1989). In discrete-time systems, conjugation is a very elementary operation on rational transfer functions that replaces some of their poles by their reflections with respect to the unit circle. With the aid ofJ-lossless conjugation conjugation by aJ.lossless system), it is shown that the parametrization of sub-optimal solutions ofH∞model-matching problems is reduced to a Lyapunov-type equation. The parametrization of all solutions is given in an extremely simple way. It is further proved that theJ-lossless conjugation of theH∞model-matching problem is a natural state-space representation of classical interpolation in discrete-time systems.