Recently, Peng and Zhang have introduced the reactant-product decoupling (RPD) equations. These are an exact formulation of quantum mechanical reactive-scattering, whereby the Schrodinger equation is partitioned into a set of uncoupled equations, each of which describes the dynamics in one arrangement of the reaction. In this paper we derive an efficient method for solving the RPD equations which is based on the Chebyshev propagator. The derivation makes use of the recently derived time-independent wavepacket version of the RPD equations. We test the method by applying it to the collinear H+H-2 reaction.