This work aims to provide additional theoretical investigation of a promising class of nondiffracting vector beams-the discrete vector frozen waves (FWs)-in the generalized Lorenz-Mie theory. The exact beam shape coefficients for unsymmetrized FWs with linear, azimuth, and radial polarizations are given in analytic form, thus extending previous derivations based on circularly symmetric Davis or aplanatic Bessel beams. Owing to their unique properties, it is believed that FWs will become important wave fields in optical tweezers, optical system alignment, remote sensing, optical bistouries, atom guiding, and so on. The present analysis is therefore fully justified.