This paper proposes a methodology to change the shape of a B-Spline curve locally. Present algorithm modifies the existing B-Spline curve and makes it pass through a given point P, constrained to lie in region R, with limited deviation from the original curve. Proposed methodology splits the curve into atmost three segments based on the curvature of the curve and then modifies only one segment using knot insertion and control point inclusion. © 2006 by CAD Solutions.