The conversion of a linear polarized laser beam into a point symmetric beam with linear dependence of the polarization on the angular position in the beam is described. The method is based on the combination of two circular polarized beams with linear phase-angular dependence. Two different optical setups are shown: a two-path scheme with one computer-generated hologram (CGH) and a one-path scheme with two polarizing computer-generated holograms (PCGH). Such polarization configurations are useful for particle acceleration, in fiber optics, laser pumping, nonlinear optics and other applications.