Abstract: Cardinal B-spline wavelets have been widely used in multi-resolution modeling for curves and surfaces.Usually,the size of coefficient matrix for the orthogonal decomposition is too large to solve and to allocate enough memory in a computer if the B-spline curve has a huge number of control vertices.Gauss algorithms for the quick decomposition of such a B-spline curve are introduced by using B-spline semi-orthogonal wavelets in the paper.