The Root Locus method of control system design was developed in the 1940's. It is a set of rules that helps in sketching the path traced by the roots of the closed loop characteristic equation of the system, as a parameter such as a controller gain, k, is varied. The procedure provides approximate sketching guidelines. Designs on control systems using the method are therefore not exact. This paper aims at a non‐graphical method for finding the exact system parameters to place a pair of complex conjugate poles on a specified damping ratio line. The overall procedure is based on the exact solution of complex equations on the PC using numerical methods.