The authors study the surface waves on a toroidal plasma in a quasistatic approximation. By taking into account the fact that plasma modes are characterized by their parity with respect to coordinate system inversion they obtain a new dispersion equation in addition to the equation studied before. Two independent groups of plasma modes exist, each group described by only one of the dispersion equations. The difference in the plasma eigenfrequencies of the two groups of modes is more pronounced for smaller aspect ratios while for larger aspect ratios both frequencies are almost indistinguishable.