In a former paper [1] the second author considered the twofold one parametric linear optimization problem with two independent parameters λ ϖ R and μ ϖ R. This paper described qualitative investigations and a procedure for solving this problem by a certain type of exhaustive algorithm which is rather difficult to handle. In the present paper the authors deal with the same problem, but now in the form   They give an alterantive algorithm which seems to be more effective than the former one. It describes a shortest route through the stability rectangles which result in solving the above problem: each rectangle is tonched only once. The authors prove that the algorithm takos care of all rectangles which can oeeur and they give an example.