<p>In this paper we derive an efficient subdivision algorithm for the binary refinement of non-uniform spline functions or curves represented in the B-spline basis. We recursively insert the new knots into the divided differences that define the B-splines. This creates sequences of intermediate divided differences from which we construct sequences of normalized B-splines. From the refinement equations for these B-splines, the subdivision algorithm follows by induction. The coefficients computed at each step of the algorithm are themselves B-spline coefficients.</p>