  The conventional absence of field renormalization in the local potential
approximation (LPA) --implying a zero value of the critical exponent \eta -- is
shown to be incompatible with the logic of the derivative expansion of the
exact renormalization group (RG) equation. We present a LPA with \eta \neq 0
that strictly does not make reference to any momentum dependence. Emphasis is
made on the perfect breaking of the reparametrization invariance in that pure
LPA (absence of any vestige of invariance) which is compatible with the
observation of a progressive smooth restoration of that invariance on
implementing the two first orders of the derivative expansion whereas the
conventional requirement (\eta =0 in the LPA) precluded that observation.
