HELIOSEISMOLOGY, the study of solar oscillations, yields information on the Sun's internal rotation and magnetism which is of great importance in understanding the 22-year solar cycle. We show here that helioseismic data suggest that the Sun's internal rotation rate, at depths greater than half the solar radius, has changed systematically during the most recent cycle. There is no variation, however, in the rotation over a range of intermediate solar radii covering the upper part of the Sun's radiative interior and the lower part of the convective zone; this intermediate region is where, according to the same helioseismic data, an abrupt change in rotation rate with depth accompanies the transition from convective to radiative structure. We suggest that the modulation of the rotation rate in the Sun's interior could be caused by a torsional oscillation, provided that a poloidal magnetic field of kilogauss strength exists in the radiative interior.