  The Ginsparg-Wilson relation $D \gamma_5 + \gamma_5 D = 2 a D R \gamma_5 D$
with $R = (a \gamma_5 D)^{2k}$ is discussed. An explicit realization of D is
constructed. It is shown that this sequence of topologically-proper lattice
Dirac operators tend to a nonlocal operator in the limit $k \to \infty$. This
suggests that the locality of a lattice Dirac operator is irrelevant to its
index.
