We study the thermodynamic properties of the high-temperature modification of fullerites on the basis of the Girifalco intermolecular potential. In the present work, using Lindemann'S melting criterion, we estimate a possible melting curve Tm(P) of C60 fullerite. To take into account the lattice anharmonicity, which has a strong effect at T < 700 K, we use the correlative method of unsymmetrized self-consistent field. To check this approach, first we have applied it to solid Ar. In the range between its triple point Tt = 83.807 K and 260 K we obtained the mean square relative deviation from experimental data of about 0.7%. The melting curve for C60 fullerite has been calculated from the melting point at normal pressure estimated at 1500 K up to 15 kbar, which corresponds to Tm = 4000 K, i.e. to the temperature estimated by Kim and Tomáek [Phys. Rev. Lett. 72, 2418 (1994)] as that of the decomposition of the C60 molecule itself. The temperature dependence of the melting pressure is approximated very well by the Simon equation(Pm(T)/bar - l)/b = (T/T0)c with T0 = 1500 K, b = 6643.8, and c = 1.209. The temperature dependence of the molar volume along the melting curve is described by Vs(T) = Vs(T)0 - 29.20 In (T/T0).