A rigorous theory was further extended for the reversing-pulse electric birefringence (RPEB) of the ionized polyion of cylindrical symmetry with the permanent dipole moment mu(3), in addition to two previously considered electric dipole moments, i.e., the root-mean-square-average moment (m(3)(2))(1/2) resulting front the fluctuation of ion-atmosphere along the longitudinal (3)axis of the polyion with a single relaxation time tau(I), as originally proposed by Szabo et al. [J. Chem. Phys. 85, 7472 (1986)], and the electronic moment from the intrinsic covalent polarizability anisotropy Delta alpha between the longitudinal and transverse axes of the polyion by Yamaoka et nl, [J. Chem. Phys. 101, 1625 (1994)]. The extended RPEB expressions were derived with three electric and hydrodynamic parameters (p = mu(3)(2)/kT Delta alpha, q = [m(3)(2)](1/2)/kT Delta alpha, and tau* = tau(l)/tau(theta)) in the Kerr-law region. Calculated with appropriate values to these parameters, the theoretical curves show such new features that either maxima or minima appear in the buildup and reverse processes. The present theory was used to analyze a set of experimental RPEB signals of poly(alpha,L-glutamic acid) in helical conformation in methanol and in methanol-water containing sodium hydroxide, By fitting the observed data to theoretical curves, the contribution of [m(3)(2)](1/2) was shown to surpass that of mu(3) for the same helical sample that was partially ionized by neutralization with sodium hydroxide.