A new transfer-matrix method is developed for low-energy-electron diffraction and other interface electronic-structure problems. This new procedure uses the waves incident on each layer as the basis for the transfer matrix. These waves are not singular at the plane of atoms, so that transfer can be done from one atom plane to the next, further from the singularities which remain at neighboring planes than in other methods. Because of the resulting more rapid convergence, this new transfer matrix can be chosen smaller than previous transfer matrices whenever interlayer scattering is strong. The convergence is further improved for strong scattering between adjacent layers by handling this scattering without approximation in a spherical-wave basis. A similar procedure is given for treating the surface region and connecting it to the semi-infinite bulk. A new procedure is also given for efficiently obtaining the bulk boundary conditions used beneath the surface from the transfer matrix. This new boundary-condition procedure is also useful in transfer-matrix methods other than the present one. © 1980 The American Physical Society.