  In this paper we give a geometric parametrization to the
Cabibbo-Kobayashi-Maskawa (CKM) mixing matrix and the Jarlskog invariant, which
is based on two flag manifolds $SU(3)/U(1)^{2}$. To treat a fourth generation
of quarks on CP violation we generalize the parametrization to one based on two
flag manifolds $SU(4)/U(1)^{3}$.
