Ab initio calculations have been employed to investigate the peculiar change in magnetic property (from diamagnetic to paramagnetic) of the dianionic ${\mathrm{C}}_{60}$-dimer phase in a rapidly cooled $A{\mathrm{C}}_{60}$ samples ( $A$: alkali metal). We first note that the triplet state of $({\mathrm{C}}_{60}{)}_2^{-2\mathrm{}}$ which was never considered previously is nearly degenerate with the singlet state, and the transition barrier between the two states is reasonably small. This explains the susceptibility increase with an increase in temperature and the magnetic phase transition in the process of the dimer to monomer phase transition.