Abstract. An important surface modeling problem in CAD is to connect two disjoint B-spline patches with the second-order geometric continuity. In this paper we present a study to solve this problem based on the surface extension algorithm [Computer-Aided Design 2002; 34:415– 419]. Nice properties of this extension algorithm are exploited in depth and thus make our solution very simple and efficient. Various practical examples are presented to demonstrate the usefulness and efficiency of our presented solution.