By examining the analyticity of a sequence of topologically-proper lattice
Dirac operators, we show that they tend to a nonlocal Dirac operator. This
implies that a nonlocal lattice Dirac operator can have exact zero modes sa
tisfying the Atiyah-Singer index theorem, in gauge backgrounds with nonzero
topological charge. (C) 2001 Published by Elsevier Science B.V.