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The main concern of classical homogeneous nucleation theory has been a thermodynamic description of initial stage of nucleation from embryo to nucleus with a little larger size over the critical one, thus, the change of parent phase in the system has been assumed to be negligible because of the largeness in volume and mass comparing that of nuclei. As a result, the nucleation curve (free energy change versus nucleus size) passes through well-known single maximum point corresponding to the critical size of the nucleus. In the present study, thermodynamics of the classical homogeneous nucleation was re-visited and developed a modified equation for multi-component solution and gas system with multi-component nuclei by taking into account the change of the free energy of parent phase. Using this equation, the calculation of nucleation curve beyond the size of critical nucleus became possible. A calculation of A–B binary solution system revealed a new minimum point in the nucleation curve, in addition to the maximum point. This minimum point indicates the theoretical possibility to stabilize a large amount of nano-nuclei in equilibrium with the supersaturated parent phase. In addition, Kelvin equation was proved at the extremum on the nucleation curve. Many scientists have misunderstood that Kelvin equation corresponds to the maximum state because they have unnoticed the presence of the minimum and its stability. At the minimum state, the nuclei should be more stable than those at the maximum state. Thus, Kelvin equation should correspond to the minimum state rather than the maximum state.