Assume that \(F(u)=\sum_{i=0}^n\,B_i^{\Delta_l,n}\,\mathbf{b}_i\) and \(G(u)=\sum_{i=0}^n\,B_i^{\Delta_r,n}\,\mathbf{c}_i\) are Bézier curves over \(\Delta_l=[r,s]\) and \(\Delta_r=[s,t]\) respectively, \(r < s < t\). \(F,G\) are \(C^k\)-continuous at \(s\) \[ \Leftrightarrow \mathbf{c}_i=\mathbf{b}^i_{n-i}(t)~\forall\,0\leq i\leq k \Leftrightarrow \mathbf{b}_{j}=\mathbf{c}^{n-j}_0(r)~\forall\,n-k\leq j\leq n \]