  We clarify the questions rised by a recent example of a lattice Dirac
operator found by Chiu. We show that this operator belongs to a class based on
the Cayley transformation and that this class on the finite lattice generally
does not admit a nonvanishing index, while in the continuum limit, due to
operator properties in Hilbert space, this defect is no longer there. Analogous
observations are made for the chiral anomaly. We also elaborate on various
aspects of the underlying sum rule for the index.
