  The standard model is reconstructed by new method to incorporate strong
interaction into our previous scheme based on the non-commutative geometry. The
generation mixing is also taken into account. Our characteristic point is to
take the fermion field so as to contain quarks and leptons all together which
is almost equal to that of SO(10) grand unified theory(GUT). The space-time
$M_4\times Z_2$; Minkowski space multiplied by two point discrete space is
prepared to express the left-handed and right-handed fermion fields. The
generalized gauge field $A(x,y)$ written in one-differential form extended on
$M_4\times Z_2$ is well built to give the correct Dirac Lagrangian for fermion
sector. The fermion field is a vector in 24-dimensional space and gauge and
Higgs fields are written in $24\times24$ matrices. At the energy of the equal
coupling constants for both sheets $y=\pm$ expected to be amount to the energy
of GUT scale, we can get $\sin^2\theta_{_{W}}=3/8$ and
$m_{_{H}}=\sqrt{2}m_{_{W}}$. In general, the equation $m\ma{H}=(4/\sqrt
{3})m\ma{W}\sin\theta\ma{W}$ is followed. Then, it should be noticed that the
same result as that of the grand unified theory such as SU(5) or SO(10) GUT is
obtained without GUT but with the approach based on the non-commutative
geometry and in addition the Higgs mass is related to other physical quantities
as stated above.
