Symmetry analysis of the low-temperature phase of RbMnCl₃ crystals with the monoclinic axis perpendicular to the sixfold axis of the high-temperature phase showed that its space group is either C_2h³ or C_2h⁶. The distribution of normal vibrations over the irreducible representations of the high-temperature phase is refined, and the symmetry relationships for normal vibrations of all possible low-temperature phases are tabulated. The model of the potential function of the crystal is obtained by the nonempirical Kim-Gordon method. This model allows one to establish the existence of the saddle point of the potential surface and several harmonically unstable modes corresponding to correlated rotations of rigid MnCl₆ and Mn₂Cl₉ polyhedra. The absolute energy minimum is determined by deforming the lattice along the eigenvector of the E_1g mode within the sp. gr. C_2h⁶.