We present new results on the polarization of the far-infrared emission from the dust ring at the center of the Galaxy. Previous far-infrared polarimetry of the region has been confined to the main ridge of emission. The new measurements cover the entire area of the ring. Polarization maps computed for magnetic fields with biaxial symmetry cannot be made to fit the data. Maps computed for axisymmetric fields provide much better fits, but the results show that the ring and field cannot both have ideal symmetry. The dispersion of the measured position angles about the directions computed from the self-similar model of Wardle & Königl (1990) is comparable to the dispersion about mean values observed in the most orderly dark clouds. The observed polarization is consistent with a model which deviates from axisymmetry by a small distortion of the field or by nonuniform distribution of the emitting dust.