[en] A model of discretized random surfaces that contains the extrinsic curvature as well as the usual area term in the action is considered. The renormalization group predicts that at large distances the model is indistinguishable from previous proposals of triangulated surfaces that contained only the area term, but, unlike them, does not grow spikes. The partition function and all its moments are finite and well defined. The model is solved for large d in the vicinity of the IR fixed point. The Hausdorff dimension is ∞ and the entropy exponent agrees with the one obtained by Zamolodchikov and others for the Polyakov action in the continuum. (orig.)