  Within one loop approximation, the renormalization group analysis of the
Higgs boson mass is performed with an initial condition induced by
$m_{_H}=\sqrt{2}m_{_W}$ which is presented in the new scheme of our
noncommutative differential geometry for the reconstruction of the standard
model. This initial condition holds at energy derived from $g^2=(5/3)g'^2$ with
the running SU(2)$_{_L}$ and U(1)$_{_Y}$ gauge coupling constants.
$\sin^2\theta_{_W}=3/8$ is obtained under same conditions. However, contrary to
${\rm SU(5)}$ GUT without supersymmetry, the grand unification of coupling
constant is not realized in this scheme. The physical mass of the Higgs boson
considerably depends on the top quark mass $m_{top}$ since the top quark Yukawa
coupling constants gives a large negative contribution to $\beta$ function of
the Higgs quartic coupling constant in wide range. The Higgs boson mass varies
from 153.42GeV to 191.94GeV corresponding to $168{\rm GeV}\leq m_{top}\leq
192{\rm GeV}$. We find $m_{_H}=164.01$GeV for $ m_{top}=175$GeV and
$m_{_H}=171.92$GeV for $ m_{top}=180$GeV.
