In system design the exact model matching problem with stability consists of compensating a given system, using a realizable control law of a specified structure, in order to ensure the stability of the compensated system and achieve a target closed-loop transfer function. In this paper we develop a novel numerical method to verify the solvability of the problem for left invertible systems and further construct a desired solution. Our method has a complexity which is cubic in the state dimension of the system and the desired model and can be implemented in a numerically reliable way. (C) 2006 Elsevier Ltd. All rights reserved.