Abstract Presented here are the photoelectron angular distribution non-dipole parameters associated with the terms of the second order O [( kr) 2] ( k is the photon energy and r is the radius of the ionized atomic shell) for both unpolarized and linearly polarized radiation. The parameters are given for atomic shells with binding energies lower than 2 keV of all elements 1 ⩽ Z ⩽ 100 for four values of photoelectron energy in the range 1−10 keV. In this range, the second-order terms are shown to make a significant contribution (up to ∼30%) to the angular differential cross section. The inclusion of these terms becomes all the more important in calculations of the differential cross section ratio for the fixed geometry of angles which is measured experimentally in the case of linearly polarized radiation. The Dirac–Fock–Slater potential is used in the calculations. The hole left by the emitted electron is taken into account in the frozen orbital approximation.