Abstract: Skin deformation based on an underlying skeleton is a common method to animate believable organic models. The most widely used skeletal animation algorithm, linear blend skinning, is also known as skeleton subspace deformation, vertex blending, or enveloping. It runs in real-time even on a low-end hardware but it is also notorious for its failures, such as the collapsing-joints artifacts. We present a new algorithm which removes these shortcomings while maintaining almost the same time and memory complexity as the linear blend skinning. Unlike other approaches, our method works with exactly the same input data as the popular linear version. This minimizes the cost of upgrade from linear to spherical blend skinning in many existing applications: the data structures and models need no change at all. The paper discusses also theoretical properties of rotation interpolation, essential to spherical blend skinning.