  We consider the question of removing the ultraviolet cutoff in a 2D Quantum
Field Theory with an interaction term which is non-renormalizable by power
counting. This model arises as the first non-trivial correction beyond the
Gaussian approximation of the so called Capillary Wave or Drumhead Model, and
is rather important from a physical point of view since it correctly describes
the finite size effects of two-dimensional interfaces. Despite the fact that
the interaction is non-renormalizable, we prove that for a large class of
regularization schemes the finite and divergent parts can be separated in a
simple way. Furthermore, the finite part is independent of the choice of cutoff
prescription used.
