  We present the general method to introduce the generalized Chern-Simons form
and the descent equation which contain the scalar field in addition to the
gauge fields. It is based on the technique in a noncommutative differential
geometry (NCG) which extends the $N$-dimensional Minkowski space $M_N$ to the
discrete space such as $M_N\times Z_2$ with two point space $Z_2$. However, the
resultant equations do not depend on NCG but are justified by the algebraic
rules in the ordinary differential geometry.
