  Liouville field theory is quantized by means of a Wilsonian effective action
and its associated exact renormalization group equation. For $c<1$, an
approximate solution of this equation is obtained by truncating the space of
all action functionals. The Ward identities resulting from the Weyl invariance
of the theory are used in order to select a specific universality class for the
renormalization group trajectory. It is found to connect two conformal field
theories with central charges $25-c$ and $26-c$, respectively.
