A novel method for finding all fractional-order (FO) proportional-integral-derivative (PID) controllers that stabilize a given system of integer or non-integer order is proposed. The stability bounds of such FO PID controllers are calculated in the frequency domain and are given in terms of the proportional gain Kp, integral gain Ki and derivative gain Kd. In this paper, they will be plotted on the (Kp, Ki) plane. A key advantage of this approach is that it provides the stability boundaries even when the transfer function of a system is not available, as long as the frequency response of the system can be obtained. An example is presented to illustrate the effectiveness of this method.