We show through numerical simulations and experimental data that a fast and simple iterative loop known as the Fienup algorithm can be used to process the measured Maker-fringe curve of a nonlinear sample to retrieve the sample's nonlinearity profile. This algorithm is extremely accurate for any profile that exhibits one or two dominant peaks, which covers a wide range of practical profiles, including any nonlinear film of crystalline or organic material (rectangular profiles) and poled silica, for which an excellent experimental demonstration is provided. This algorithm can also be applied to improve the accuracy of the nonlinearity profile obtained by an inverse Fourier transform technique.