The preequilibrium statistical model, which is used to analyze nuclear reaction data, depends basically on number of parameters including the master equation. A numerical solution for the master equation of the preequilibrium statistical model is presented in this work. One-component Fermi gas model is assumed. This numerical method is shown to give the same accuracy for the simple as well as the more advanced schemes. The present method shows fast convergence for a wide range of physical system parameters. Such a method is applied for two reaction examples that include neutron and proton induced reactions with 54Fe nucleus for entrance energies 20 and 80 MeV. Comparisons with standard solution methods show that the method suggested here reveals its accuracy and simplicity for practical applications and calculations. The results indicated that the present method is proper for low reaction energies, but with worse accuracy at higher energies. The behavior of the present method was examined against the energy, exciton numbers, and time variation.