  Normality in connection with $\gamma_5$-hermiticity determines the basic
chiral properties and rules. The Ginsparg-Wilson (GW) relation is one of the
allowed constraints on the spectrum. Interrelations between features of the
spectrum, the sum rule for chiral differences of real modes and contributions
to the Ward identity are pointed out. The alternative chiral transformation of
L\"uscher gives the same Ward identity as the usual one, in the global and in
the local case. Imposing normality on a general function of the hermitean
Wilson-Dirac (HWD) operator, inevitably leads at the same time to the Neuberger
operator and to the GW relation. In this context also the case with zero
eigenvalues of the HWD operator is handled. The eigenvalue flows of the HWD
operator obey a differential equation the characteristic features of the
solutions of which are discussed.
