Given a characteristic polynomial dependent on two parameters and a root region D in complex plane, the set of parameters that ensures all roots of the polynomial lie within D is considered. The set of interest is called D-stable region, or the stability set. The problem can be partially solved by well-known D-partition technique, which yields overall boundary that contains the boundary of the stability set. A constructive algorithm is proposed to extract the exact boundary of the stability set, given that the polynomial depends linearly on the parameters, and the boundary of the root region D is a piecewise rational curve in complex plane. Under these assumptions, the boundary of the stability set consists of parts of rational curves, and parts of lines (line segments, rays), thus being formed from piecewise rational curves as well. If, moreover, the stability set is constrained by the user within some box, then its boundary can be described by set of rational curve parts and line segments, defined on finite parameter segments. The proposed algorithm depends on a single auxiliary procedure: the calculation of real root for real polynomials.