A method is proposed for constructing appropriate sets of special points in the Brillouin zone in which the extended unit cell method is used with a subsequent shift from the center of the reduced Brillouin zone. The proposed method offers several advantages over the commonly used Monkhorst-Pack method. The difference in the construction of sets of special points for the direct and reciprocal lattices is discussed for crystals belonging to a nonsymmorphic space group. The cases of a planar square lattice and an fee lattice are considered to illustrate general results.