Several widely used neutron transport codes approximate the fission-source matrix by accepting only a single fission-neutron spectrum, regardless of how this spectrum is selected. This approximation introduces a needless calculational error. To overcome this flaw the difference between the correct and the approximate fission source matrices should be added to the scattering matrix. This significantly reduces the calculational errors in integral parameters calculated in the k formulation of the stationary transport equation and eliminates these errors altogether when the integral parameters are calculated in the other formulations of the equation. A numerical example is provided to demonstrate these points. The reactivity k, the average neutron energy , and the ratio are calculated for a JEZEBEL-like assembly using the standard and the proposed procedures.