The feasibility of Levenberg-Marquardt method, modified for the case of inaccessibility of a priori covariance matrices for methane vertical profiles, for atmospheric methane total column amount retrieval from the spectra measured by IASI/METOP is studied. The method and algorithm were implemented into software package together with iterative evaluation of a posteriori covariance matrices and averaging kernels for each individual case of retrieval. This allows selection of the results on the basis of properties of both matrices. The comparison between our results and IASI standard methane products retrieved from the same spectra shows their satisfactory agreement.