In this work, the problem of interpreting linear marine magnetic anomalies in the context of the spreading model is considered. Based on the least squares method, a new algorithm for determining the position of direct and reverse polarity blocks is proposed. The global minimum of the residual is found by a combination of the multistart and Monte Carlo methods. Using an example of a field of three blocks perturbed by a normal noise, it is shown that the method yields an error close to the minimum possible. Using a model constructed by the inversion scale, it is revealed that the proposed algorithm allows one to find positions of block boundaries of the field without noise with a higher accuracy determined in fact by the computation time.