We compute one and two loop quadratic divergent contributions to the bare Higgs mass in terms of the bare couplings in the Standard Model (SM). We approximate the bare couplings, defined at the ultraviolet cutoff scale, by the MSbar ones at the same scale, which are evaluated by the two loop renormalization group equations for the Higgs mass around 126GeV in the SM. 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.