A locally exact numerical scheme (LENS) based on the concept of locally exact numerical differencing is presented. The essence of the LENS scheme consists in determining the coefficients of the difference scheme so that the resulting equation interpolating numerical fluxes at the control volume surface satisfies the analytical solution of transport equations with absorption and source terms. The spatial distribution of the coefficients of transport equations is taken into consideration based on a four-region model among three adjacent control volumes, in which continuous conditions for solutions are imposed on the boundary between two adjacent regions. An analysis of nonoscillation properties of the present LENS scheme was performed using the characteristic polynomial analysis method. It was found that the LENS scheme possesses the potential for nonoscillation properties for stationary convection-diffusion equations with absorption. The LENS scheme is examined through numerical experiments and shows stable and accurate solutions for transport equations with absorption and source terms.