An improvement in the approximation of the spatial distribution of the source term in the PALLAS discrete-ordinates code by a combination of linear and exponential functions results in a reduction of numerical errors compared with those due to the use of only a linear approximation based on a direct integration method. The results obtained by the improved approximation for one-dimensional radiation transport calculations are compared with those by the PALLAS code with the original linear approximation and by the SN code ANISN. For further verification, this improved approximation is applied to two-dimensional neutron transport calculations, in which numerical errors due to the spatial mesh sizes used in the calculations are studied. As a result, it is found that the use of the improved approximation gives reasonable solutions with small numerical errors, irrespective of the spatial mesh size in both one- and two-dimensional PALLAS calculations of radiation transport.