A technique for measuring the current-voltage characteristics (IVC) of a nonlinear inertia-free element from the amplitude spectrum of a current curve obtained by decomposing it into a Fourier series is given. The initial data for the method are the curves of current and voltage on a nonlinear element, measured for different points in time. The IVC is represented as a ratio of power polynomials whose coefficients are determined by the Cholesky method. Examples of measurement of the current-voltage characteristics are given, estimates of the relative and absolute error of the approach are given. The advantage of the proposed approach in comparison with the existing ones is the better accuracy of the reproduction of the IVC.