  We study flow of renormalization group (RG) transformations for the massless
Gross-Neveu model in a non-perturbative formulation. The model is defined on a
d=2 dimensional Euclidean space with a finite volume. The quadratic
approximation to the flow stays bounded after suitable renormalization. We show
that for weak coupling this property also is true for the complete flow. As an
application we prove an ultraviolet stability bound for the model. Our
treatment is an application of a method of Bauerschmidt, Brydges, and Slade.
The method was developed for an infrared problem, and is now applied to an
ultraviolet problem.
