This paper presents an algorithm for extending B spline carves and surfaces. Based on the unclamping algorithm for B-spline curves, we propose a new algorithm for extending B spline curves that extrapolates using the recurrence property of the de Boor algorithm. This algorithm provides a nice extension, with maximum continuity, to the original curve segment. Moreover, it can be applied to the extension of B spline surfaces. Extension to both single and multiple target points/curves are considered in this paper.