Starting with the fact that the optimum in any linear programming problem over a certain. bounded region ist attained in at least one feasible basic solution, and that the number of feasible basic solutions is finite, the general linear programming problem is considered as a combinatorial programming problem. In order to solve this problem the extension principle die to Schoch is applied. According to the set S of feasible basic solutions of the original problem, a set R is defined which contains S. By successive reduction of the objective function, a sequence of subsets Uν R is formed. Moreover, a properly monotone increasing sequence bν of lower bounds for the value of the objective function is given. By making use of a discrepancy function, the author investigats, whether Uν and S have a non-empty intersection. the fitst non-empty intersection Uν ∩ S which can be found represents the set of all optimal basic solutions of the initial problem.