  We consider the exact renormalization group for a non-canonical scalar field
theory in which the field is coupled to the external source in a special non
linear way. The Wilsonian action and the average effective action are then
simply related by a Legendre transformation up to a trivial quadratic form. An
exact mapping between canonical and non-canonical theories is obtained as well
as the relations between their flows. An application to the theory of liquids
is sketched.
