Vectorial properties of finite electromagnetic beams are described by a global characteristic unit vector and the generalized Jones vector. A parallel characteristic unit vector to the propagation axis corresponds to the cylindrical vector beam. The cylindrical vector beams in the transmission are described by the representation theory in the paraxial approximation. It is found that the characteristic unit vector changes in the transmission, which is neither parallel nor perpendicular to the propagation axis. The change of the characteristic unit vector causes a displacement perpendicular to the incidence plane, and the displacement depends on the polarization ellipticity. The differently circularly (left and right) polarized light beams undergo opposite displacement. Similar to the previously observed so-called spin Hall effect of uniformly polarized beam, spin Hall effect of cylindrical vector beam could also be generated in the transmission.