A new method is presented for the description of multiple elastic scattering of low-energy electrons from ordered overlayers adsorbed on periodic substrates. By separating, in the exact multiple-scattering series, the scattering events that occur within the overlayer from those in the substrate, it is possible to treat the geometrical structure of the overlayer independent of the Bravais net of the underlying substrate layers. Consequently, the dynamical scattering cross section is expressed entirely in terms of layer scattering matrices of the substrate, which thereby avoids the more time-consuming sublattice formalism that has been used in previous exact calculations of diffraction intensities.