  We note that Fujikawa's proposal of generalization of the Ginsparg-Wilson
relation is equivalent to setting $R = (a \gamma_5 D)^{2k}$ in the original
Ginsparg-Wilson relation $D \gamma_5 + \gamma_5 D = 2 a D R \gamma_5 D$. An
explicit realization of D follows from the Overlap construction. The general
properties of D are derived. The chiral properties of these higher-order (k >
0) realizations of Overlap Dirac operator are compared to those of the
Neuberger-Dirac operator (k = 0), in terms of the fermion propagator, the axial
anomaly and the fermion determinant in a background gauge field. Our present
results (up to lattice size 16 x 16) indicate that the chiral properties of the
Neuberger-Dirac operator are better than those of higher-order ones.
