Summary: In terms of the uniform \(B\)-spline and Bézier representations which were proposed by L. Romani and M. A. Sabin [Comput. Aided Geom. Des. 21, No. 6, 549–560 (2004; Zbl 1069.65532)], we study the problem of the conversion between uniform rational \(B\)-spline and rational Bézier representations. The main ideal is to combine the conversion matrix and weight factors to transform the control points of rational \(B\)-spline curves into the control points of rational curves and vise versa.