The melting curve of AuGa\(_2\) have been calculated up to 30 GPa using first principles calculations based on the density functional theory. We use the Z method approach and apply a Bayesian analysis to correct the prediction the melting points. The fluorite, cottunite and monoclinic phases of are considered. For pressures below....... the melting temperature of the.... phase is the lowest one, and the melting curve is decreasing. The results have good agreement with experimental data, and we show that the negative Clapeyron slope is directly related to the direction of each Z curve, as has been seen for other materials (cite Lithium, by Dafang Li). In addition, we provide analytic expressions for both intervals of the melting curve: \(T=T_1(1+P/a)^be^{-cP}\) for the decreasing part, and \(T=T_2(1+P/d)^e\) for the increasing interval.