Abstract: The problem of exercising the freedoms of reparameterization of polynomial curve segments to achieve a "parametric flow" closest to the unit-speed or arc-length representation is addressed.A new quantitative measure of "closeness" to arc-length parameterization is presented and according to this measure,the problem of identifying the optimum rational reparameterization of a degree n polynomial curve is shown. The advantage of this measure is that the optimum rational reparameterization's parametric speed satisfies that the maximum deviation from unity is the minimum in this family.Experiments for comparing the efficiency of this algorithm with other methods are also included.