In the case, where a given linear optimization problem is soluble, the simplex procedure due to DANTZIG leads after a finite number of steps to a, certain solution (to an optimal base-point), but thereby the question concerning the unicity of the solution is not answered. The intention of this paper is to give necessary and sufficient conditions for the unicity of .the solution in such a manner, that the unicity can be stated from the last tableau of the procedure. The case of degeneration should not be excluded.