what is meant "an initial stable completion" in this text? I don't understand meaning. In this paper a construction of C1-wavelets on the two-dimensional sphere is presented. First, we focus on the construction of a multiresolution analysis leading to C1-functions on S2. We show refinability of the constructed tensor product generators. Second, for the wavelet construction we employ a factorization of the refinement matrices which leads to refinement matrices characterizing complement spaces. With this method we achieve an initial stable completion. A desired stable completion can be gained by lifting the initial stable completion. The result is a biorthogonal wavelet basis leading to C1-functions on the sphere.