  We use the Schwinger-Dyson equations as a starting point to derive
renormalization flow equations. We show that Katanin's scheme arises as a
simple truncation of these equations. We then give the full renormalization
group equations up to third order in the irreducible vertex. Furthermore, we
show that to the fifth order, there exists a functional of the self-energy and
the irreducible four-point vertex whose saddle point is the solution of
Schwinger-Dyson equations.
