The Ginsparg-Wilson relation D gamma (5) + gamma D-5 = 2aDR gamma D-5 with
R = (a gamma D-5)(2k) is discussed. An explicit realization of D is constru
cted. It is shown that this sequence of topologically-proper lattice Dirac
operators tend to a nonlocal operator in the limit k --> infinity. This sug
gests that the locality of a lattice Dirac operator is irrelevant to its in
dex.