Since Doo-Sabin and CatmulI-Clark surfaces were proposed in 1978, eigenstructure, con-vergense and continuity analyses of stationary subdivision have been performed very well, but it has been very difficult to prove the convergence and continuity of non-uniform recursive subdivision surfaces (NURSSes, for short) of arbitrary topology. In fact, so far a problem whether or not there exists the limit surface as well as G1 continuity of a non-uniform Catmull-Clark subdivision has not been solved yet. Here the concept of equivalent knot spacing is introduced. A new technique for eigenanalysis, convergence and continuity analyses of non-uniform CatmulI-Clark surfaces is proposed such that the convergence and G1 continuity of NURSSes at extraordinary points are proved. In addition, slightly improved rules for NURSSes are developed. This offers us one more alternative for modeling free-form surfaces of arbitrary topologies with geometric features such as cusps, sharp edges, creases and darts, while elsewhere maintaining the same order of continuity as B-spline surfaces.