In the preceding paper(Prog.Theor.Phys.108(2002)929 or hep-ph/0207255), we
have shown that the critical line of the first order chiral transition of QCD
can have two endpoints. In this addendum, we elucidate the mechanism to realize
the two-endpoint structure in the QCD phase diagram and argue the robustness
for the appearance of such an interesting phase structure