Abstract: In this paper we propose an algorithm, called Directrive Perturbation (PD-Algorithm), which decrease the maximum value of the absolute errors of a fitting formula obtained by a Least-Squares Method. Applying the algorithm we can increase the accuracy of the uniform approximation of the fitting formula with the original data (x_i, f(x_i)) (i=1, 2, …, m). Further, after applying a finite number of times of the perturbation, we can obtain the formuala of Tchebycheff approximation.