  In this paper we provide an analytical procedure for explicit calculation of
the left and right invariant vector fields and one-forms on SU(N) manifold. The
calculations are based on the coset parametrization of SU(N) group. The results
enable us to calculate the invariant measure or Haar measure on the group. As
an illustrative example, we calculate invariant vector fields and one-forms on
SU(2) group.
