Summary: Two arbitrarily given curves \(k_1(t)\) and \(k_2(t)\) are blended to a third curve \(b(t)\) so that \(b\) joins \(k_1\) and \(k_2\) in given points \(A_1\) and \(B_2\) \(C^l\)- and \(C^m\)-continuously, respectively. In order to meet this objective we use polynomial functions \(\alpha_{lm}(t)\) for the blending process. The Casteljau algorithm for curves is used in a special way to build the blended curve \(b(t)\). Furthermore we can use our construction to generate interpolating spline curves.