We show how the exact renormalization group for the effective action w
ith a sharp momentum cutoff, may be organized by expanding one-particl
e irreducible parts in terms of homogeneous functions of momenta of in
teger degree (Taylor expansions not being possible). A systematic seri
es of approximations - the O(p(M)) approximations - result from discar
ding from these parts, all terms of higher than the M(th) degree. Thes
e approximations preserve a field reparametrization invariance, ensuri
ng that the field's anomalous dimension is unambiguously determined. T
he lowest order approximation coincides with the local potential appro
ximation to the Wegner-Houghton equations. We discuss the practical di
fficulties with extending the approximation beyond O(p(0)).