Deformable surfaces have many applications in surface reconstruction, tracking and segmentation of range or volumetric data. Many existing deformable surfaces connect control points in a predefined and inflexible way. This means that the surface topology is fixed in advance, and also imposes severe limitations on how a surface can be described. For example a rectangular grid of control points cannot be evenly distributed over a sphere, and singularities occur at the poles. In this paper we introduce a new (G continuous) deformable surface. In contrast to other methods this method can represent a surface of arbitrary topology, and do so in an efficient way. The method is based on a generalization of biquadratic B-splines, and has a comparable computational cost to methods based on traditional tensor product B-splines.