  Normality and $\ga$-hermiticity are what gives rise to chiral properties and
rules. The Ginsparg-Wilson (GW) relation is only one of the possible spectral
constraints. The sum rule for chiral differences of real modes has important
consequences. The alternative transformation of L\"uscher gives the same Ward
identity as the usual chiral one (if zero modes are properly treated). Imposing
normality on a general function of the hermitean Wilson-Dirac operator $H$
leads at the same time to the GW relation and to the Neuberger operator.
