Rational B-splines have become the new standard for representing free-form curves and surfaces. This paper presents a method for approximating rational B-splines using digitised data. Instead of using the classical optimisation approach to solve the multivariable nonlinear equations, a new method based on iterations of least-squares solutions and single variable mimimisation is developed. This is made possible by modifying the original objective function to avoid the rational format. Simulation of fitting a 90° arc shows that the algorithm can produce accurate solutions close to nominal values. The efficiency of the algorithm also makes it possible to apply the method to day-to-day reverse engineering problems using rational B-splines.