Closed-loop identification of the ultimate gain (K-u) and critical frequency (omega(u)) of a feedback control loop is studied. The accuracy of the Astrom-Hagglund autotuner is discussed, and a simple method of improving the accuracy of the commonly used procedure is proposed and tested by simulation, A modification of the method where the traditional one-parameter relay is replaced by a two-parameter nonlinearity is also proposed. Because the selection of the two parameters of such a nonlinearity is nontrivial, an iterative procedure for the identification of K-u and omega(u) is proposed. The procedure has been found to be convergent and to give reliable and accurate identifications in a number of examples typical of chemical engineering.