While the LAPW basis functions are used to represent the valence states, core electron states, which are completely confined within a MT sphere, are calculated for the spherically averaged potential on radial grids, for each atom separately applying atomic boundary conditions. Semicore states, which are still localized but slightly extended beyond the MT sphere boundary, may either be treated as core electron states or as valence electron states. For the latter choice the linearized representation is not sufficient because the related eigenenergy is typically far away from the energy parameters. To resolve this problem the LAPW basis can be extended by additional basis functions in the respective MT sphere, so called local orbitals (LOs). These are tailored to provide a precise representation of the semicore states.