The purpose of this paper is two fold. First, we shed some light on the slow convergence behaviour of a certain iterative procedure for solving the reflection matrix in a nonmultiplying half-space. In particular, we show that the asymptotic convergence rate of the iterative procedure of Shimiju and Aoki is 1 – □1–c. Herec, 0 ≤c≤ 1. the expected number of particles emerging from a collision. Second, a convergence accerelation procedure is proposed. The asymptotic convergence rate of the accerelation procedure is given. Some very satisfactory numerical results are also presented.