A universal statement is obtained for solving linear programming problems of high order with the constraint rnatrix having arbitrary block structure and with certain order relations in the set of biocks. An algorithm based on this statement is cocstructed, using in each step of the simplex transfomation the partition, f the basis matrix into the product of two matrices having block-triangle structure. The difficuilties occuring :in the numerical procedure depend mainly on the maximal length of the chains of the ordered set of blocks.