Abstract: Based on Tchebycheffs alternation theorem for the best uniform approximation, the present paper puts forward a cross-chord method for the best fittingof quadratic polynomials to experimental data. The often-used method for thiskind of fitting was proposed by Remes, which calls for the establishment with renewed alternating points, and solution of a system of linear, equations of four unknowns. Being rather complicated, this can only be performed in a digital computer by a specially-written program. Though the cross-chord method developed in this paper requires the same kind of work to be done, it deals with the equations in which there are only two unknowns and the cancellation of the unknowns can be done very easily.Thus the computational work is reduced greatly, and even can be. carried out manually. This method is very easy for the engineering people to grasp the fitting of quadratic polynomials to experimental data. An apparent one of the applications of this method is to help determine the independent conformity of instruments and transducers.