The well-known DANTZIG-WOLFE decomposition method is a little extended so that immediately follows the finiteness of a solution method, consisting in its repeated applicatiolns to the submitted satellit programs. The method is proposed to solve linear programming problems with staircase st,ruct,ure in t,he restrictions. Hereby a series of problems connected with each other is obtained. Their number is defined by the number of steps and the dimension is determined by the altitude of steps. The solution precess is effieicnt if the steps are weakely linked The paper is concluded with an esample.