A method for improving the accuracy of radiative energy source term predictions of the classical discrete transfer method, is proposed. It is based on computation of radiative energy source terms by firing rays from medium-grid points, tracing the rays back from points of intersection with the walls to the medium grid paints and utilising the radiative energy conservation equation as opposed to tracing rays fired from surface grid points with subsequent summation of contributions from all the rays which happens to traverse the control volumes. The proposed method was then applied to the predictions of the radiative energy source term distributions of a box-shaped enclosure problem based on data reported previously on a large scale experimental furnace with steep temperature gradients typically encountered in industrial furnaces. The rectangular enclosure under consideration has interior black walls and an absorbing-emitting medium of constant properties. The predictive accuracy of both the discrete transfer method with the proposed improvement and classical discrete transfer method were evaluated by comparing their predictions with exact numerical solutions produced previously for the same enclosure problem. Comparisons of the point values of radiative energy source terms show that the proposed method provides better agreement with the exact solutions for medium grid points near the corner of the enclosure, where the classical discrete transfer method produces the largest errors. However, this increase in accuracy is only obtained at the expense of computational economy.