  We compute one- and two-loop quadratic divergent contributions to the bare
Higgs mass in terms of the bare couplings in the Standard Model. We approximate
the bare couplings, defined at the ultraviolet cutoff scale, by the MS-bar ones
at the same scale, which are evaluated by the two-loop renormalization group
equations for the Higgs mass around 126GeV in the Standard Model. We obtain the
cutoff scale dependence of the bare Higgs mass, and examine where it becomes
zero. We find that when we take the current central value for the top quark
pole mass, 173GeV, the bare Higgs mass vanishes if the cutoff is about
10^{23}GeV. With a 1.3 sigma smaller mass, 170GeV, the scale can be of the
order of the Planck scale.
