It is well known that the Routh stability criterion (RSC) is a powerful method for analyzing control system stability. A new RSC finding that can aid the tangent analysis method (TAM) to determine the necessary conditions for multiplicity is presented. Adding RSC to TAM can find the bifurcation start point which cannot be obtained using TAM alone. To the author's knowledge, the above new RSC application has not been discussed in past literatures. Our results are helpful for chemical reactor design. We used two examples of the binary reaction in a non-adiabatic CSTR to demonstrate the merit of our methods.