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,

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... e 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.