We describe a novel convenient technique to allow for the accurate measurement of the dispersion coefficients till fourth-order in the zero-dispersion wavelength region of single-mode optical fibers. The proposed method is based on a careful spectral analysis of modulation instability occurring in both normal and anomalous dispersion regime and the associated dispersive waves emitted by soliton fission. It simply requires a high-power tunable continuous-wave fiber laser and an optical spectrum analyzer and is able to retrieve both the sign and magnitude of dispersion coefficients with enhanced precision