In order to probe into classification and recognition method for planar figures in effect, a class of complete orthogonal piecewise k-degree polynomials, so-called U-system, is introduced. U-system is a class of complete orthogonal piecewise k-degree polynomials in L²[0,1]. The expansion in U-series has advantageous properties for approximations in both quadratic norm and uniform. Based on U-system, new U descriptors are defined, and the property of U descriptors and its proof are presented. To classify and recognize figures, a new normalized U descriptor is defined, which is invariant in the rotation, translation and scale transform. The experimental results show the accuracy and efficiency of new normalized U descriptors in classification and recognition method for planar figures.