In this paper, ideas from iterative feedback tuning (IFT) are incorporated into relay auto-tuning of the proportional-plus-integal-plus-derivative (PID) controller. The PID controller is auto-tuned to give specified phase margin and bandwidth. Good tuning performance according to the specified bandwidth and phase margin can be obtained and the limitation of the standard relay auto-tuning technique using a version of Ziegler-Nichols formula can be eliminated. Furthermore, by using common modelling assumptions for the relay system, some of the required derivatives in the IFT algorithm can be derived analytically. The algorithm was tested in the laboratory on a coupled tank and good tuning result was demonstrated.