  Renormalization group equation (RGE) of the Higgs mass up to one-loop order
is derived in $R_\xi$ gauge with dimensional regularization method (DREG) base
on MS (or $\bar{\rm{MS}}$) scheme. Scale-dependent properties of the Higgs mass
up to two-loop level are investigated. The result gives the positive Higgs mass
up to energy scale around the Planck scale. While following the vacuum
stability argument, the Higgs mass need to be negative above the energy scale
$10^{10}$ GeV for $M_{t}=173.3$ GeV. The conflict is induced by the
renormalization of vacuum energy value(VEV).
