Computation of the real structured singular values μ has been known to be important for stability analysis of linear systems with structured uncertainty. The authors have proposed a method to obtain an upper bound and a lower bound of the real μ by Stability Feeler which is a tool for robust stability analysis proposed by the first author. In this paper we propose a region splitting and expanding method to reduce the conservativeness of the derived upper bound and lower bound. A numerical example show that the obtained results are nearly equal to the exact value of the real μ, which are less conservative than that derived by the other methods.