  We investigate a bifurcation of periodic instanton in Euclidean
action-temperature diagram in quantum mechanical models. It is analytically
shown that multiple zero modes of fluctuation operator should be arised at
bifurcation points. This fact is used to derive a condition for the appearance
of bifurcation points in action-temperature diagram. This condition enables one
to compute the number of bifurcation points for a given quantum mechanical
system and hence, to understand the whole behaviour of decay rate. It is
explicitly shown that the previous criterion derived by nonlinear perturbation
or negative-mode consideration is special limit of our case.
