Abstract: A new method, the branch matrix algorithm, for the computer fitting of Lorentzan's experimental spectrum is suggested. It is derived from the analysis of the modified interrelations among the peak parameters of the Lorentzan curve in the iterative process for the microcomputer fitting of the Mössbauer spectrum and the treatment of the matrix branching to the algebraic equations of the Gauss Newton algorithm. The experience on the fitting of the Mössbauer spectrum indicated that in comparison with the algorithm without matrix inversion (Slavic Algorithm) the branch matrix algorithm presented in this paper has a faster convergent speed, a near iterative time and a near occupied computer memory.