This work is concerned with the algorithm of generating a new circular are interpolation. This research presents a new biarc curve fitting that is a circular interpolation method based in a triarc curve fitting. The triarc method, where a segment span is composed of three circular arcs, using maximum error estimation has the advantage of generating arc splines easily to a given tolerance. The new biarc method is called when the adjacent radii are the same in the triarc method. In generating the machining data for various cam curnves in CNC machining with the biarc method and the new biarc method, the latter accomplished faster NC-code generation, shorter NC-code block formation and machined the same cam profile more efficiently.