The recently developed Doubly Linked Face List (DLFL) structure introduces a powerful modeling paradigm that allows users to alternatively apply topological change operations and subdivision operations on mesh structure. Moreover, the DLFL is topologically robust in the sense that it always guarantees valid 2-manifold surfaces. In this paper, we further study the relationship between DLFL structure and subdivision algorithms. The paper has three contributions. First, we develop a new corner cutting scheme, which provides a tension parameter to control the shape of subdivided surface. Second, we develop a careful and efficient algorithm for our corner cutting scheme on the DLFL structure that uses only the basic operations provided by the DLFL structure. This implementation ensures that our new corner cutting scheme preserves topological robustness. The comparative study shows that the corner cutting schemes create better handles and holes than Catmull-Clark scheme.