  We discuss the weak coupling expansion of massless QCD with the Dirac
operator which is derived by Neuberger based on the overlap formalism and
satisfies the Ginsparg-Wilson relation. The axial U(1) anomaly associated to
the chiral transformation proposed by Luscher is calculated as an application
and is shown to have the correct form of the topological charge density for
perturbative backgrounds. The coefficient of the anomaly is evaluated as a
winding number related to a certain five-dimensional fermion propagator.
