  We show that the integral of the first Pontrjagin class is given by an
integer and it is identified with instanton number of the U(n) gauge theory on
noncommutative ${\bf R^4}$. Here the dimension of the vector space $V$ that
appear in the ADHM construction is called Instanton number. The calculation is
done in operator formalism and the first Pontrjagin class is defined by
converge series. The origin of the instanton number is investigated closely,
too.
