In this paper, we present a new technique called Trapezium Drawing to improve surface mesh quality while maintaining essential surface characteristics. In contrast to previous methods we do not tend to preserve mesh vertices on the original discrete surface. Instead our approach allows to keep a resulting mesh close to the surface approximated by the initial mesh. All operations are performed directly on the surface. As a result our technique is robust and runs at interactive speeds. It can be applied to triangular and quadrilateral meshes iteratively. Various quantitative measures are presented to demonstrate effectiveness of proposed technique.