  The scheme previously proposed by the present authors is modified to
incorporate the strong interaction by affording the direct product internal
symmetry. We do not need to prepare the extra discrete space for the color
gauge group responsible for the strong interaction to reconstruct the standard
model and the left-right symmetric gauge model(LRSM). The approach based on
non-commutative geometry leads us to presents many attractive points such as
the unified picture of the gauge and Higgs field as the generalized connection
on the discrete space; Minkowski space multipied by N-points discrete space.
This approach leads us to unified picture of gauge and Higgs fields as the
generalized connection. The standard model needs N=2 discrete space for
reconstruction in this formalism. \lr is still alive as a model with the
intermediate symmetry of the spontaneously broken SO(10) grand unified
theory(GUT). N=3 discrete space is needed for the reconstruction of LRSM to
include two Higgs bosons $\phi$ and $\xi$ which are as usual transformed as
(2,2*,0)$ and (1,3,-2) under left-handed SU(2)x right-handed SU(2)x U(1),
respectively. xi is responsible to make the right handed-neutrino Majorana
fermion and so well explains the seesaw mechanism. Up and down quarks have the
different masses through the vacuum expectation value of phi.
