A method of first principle calculation of alloy phase diagram was developed by the combination of first principle energy band calculation, cluster expansion method (CEM) and Monte Carlo (MC) simulation, where the effective multi-body potential energy for the flip test in MC simulation was obtained by the decomposition of the total energy by CEM. This method was applied to Cu-Au binary system. The calculated phase diagram agreed with that of CVM by introducing the dependence of the lattice constant on the concentration of the whole system. Furthermore an attempt of introducing the effect of local lattice relaxation was performed by the consideration of the local concentration. The order-disorder transition temperature became closer to the experimental value by adjustment of the local lattice constant depending on the concentration in the local region consisted of up to the second nearest neighbors of the atom tested for flipping.