Abstract: The algorithm is based on knot removal, knot insertion, and weight modification of the NURBS. These knots and weights are selected automatically by means of a fairness criterion. The proposed algorithm includes Farin's algorithm as a special case. The advantages of the new algorithm compared with Kjellander's algorithm are: 1) It is automatic, no user interaction is required. 2) It is local, each time the algorithm is applied, at most three control vertices are affected. 3) It is ensured that the fairing curve will be exactly C³ at the offensive knot location. 4) It preserves the local convexity property of the initial curve.