The problem of stabilizing a corrugated theta pinch having high β with respect to long-wave perturbations with m = 1 is considered. The suggestion of Ribe and Riesenfeld that the variable axial high-frequency current, excited in the plasma column in addition to the azimuthal current, should be used for this purpose is discussed. It is shown that the stabilizing effect may result, in this case, only from the interaction of the axial current with the conducting wall surrounding the pinch. Consideration is also given to the possibility of suppressing the m = 1 mode with a quadrupole magnetic field. The stabilizing effect is, under these conditions, due to the interaction of the quadrupole field with the axial high-frequency current and to the presence of a magnetic well formed by the quadrupole field.