Some properties of robust procedures for summarizing an additive structure of a matrix are discussed. The method of median polish introduced by \textit{J. W. Tukey} [Exploratory data analysis (1977; Zbl 0409.62003)] is an algorithm for smoothing data in two-way tables in which each iteration lowers the \(L_ 1\) norm of the residual. As a rule, the algorithm converges in a finite number of steps, but in general it does not converge to the least \(L_ 1\) norm residual. An algorithm that converges in a finite number of steps for any data and gives the \(L_ 1\) norm residual is proposed. Some examples are considered.