As a continuation of our previously published works, the metastable phase diagram of the Blume-Emery-Griffiths model is presented in addition to the equilibrium phase diagram by using the lowest approximation of the cluster variation method. We also calculate the phase transitions for the unstable branches of order parameters. The calculated first- and second-order phase boundaries of the unstable branches of the order parameters are superimposed on the equilibrium phase diagram and metastable phase diagram. It is found that the metastable phase diagram and the first- and second-order phase boundaries for the unstable branches of order parameters always exist at the low temperatures, which are consistent with the experimental and theoretical works. (C) 2000 American Institute of Physics. [S0021- 9606(00)51337-3].