A rigorous theory is formulated for the reversing-pulse electric birefringence (RPEB) for the ionized macroion of cylindrical symmetry, according to the idea of the coupled rotational (with the molecular relaxation time tau(theta)) and ion-atmosphere dynamics of rodlike macroion, developed previously by Szabo et al. [J. Chem. Phys. 85, 7472 (1986)]. The present theory is based on the interaction of applied electric pulse with two electric dipole moments of the macroion; one is due to the ion-atmosphere polarizability alpha(3) with a single relaxation time tau(I) for the distortion of ion-atmosphere along the longitudinal axis, as originally proposed, and the other is newly considered as being due to the intrinsic molecular, or instantaneously field-induced, polarizability anisotropy Delta alpha’ between the longitudinal and transverse axes of the macroion. The RPEB expressions were derived with the electric and hydrodynamic parameters (alpha(3)/Delta alpha’ and tau(I)/tau(theta)) for the low-field region. Theoretical curves were calculated with appropriate values to those parameters. The curves show some new features, i.e., either a maximum or a minimum in the buildup and reverse processes, that were not revealed in the Szabo et al. theory. The present theory was used to analyze an experimental RPEB signal of montmorillonite clay suspension. The contribution of the permanent electric dipole moment of the disklike clay particle to field orientation was ruled out.