A numerical method that is free from all spatial truncation errors is developed for one-group slab-geometry discrete ordinates problems. The unknowns in the method are the cell-edge and cell-average angular fluxes, and the numerical values obtained for these quantities are those of the analytic solution of the discrete ordinates equations. The method is based on the use of the standard balance equation, which holds in each spatial cell and for each discrete ordinates direction, and a nonstandard auxiliary equation that contains a Green’s function for the cell-average angular flux in terms of the incident angular fluxes on the cell edges and the interior source. Numerical results are given to illustrate the method’s accuracy.