A new a1gorithm of (C²-Continuous) convexity preserving cubic parametric interpo1ation curves is derived. the construction of the a1gorithm is 1oca1. The calcu1ation invo1ved is simp1e and efficient. The a1gorithm is a1so approriate for both closed curves and open curves. Finally a few examp1es of curve construction are given.