A novel and simple procedure to improve the accuracy of the measurement of the third-order Kerr non-linear coefficient of optical fibers based on self-phase modulation is described. It includes an efficient method to identify the chirp of the input pulse. A standard single-mode fiber and a highly non-linear microstructure chalcogenide fiber have been measured. The accuracy of the measurement is increased to ±5% instead of ±19% with the classical self-phase modulation method in this case.