Relay experiment can be used to identify exact model parameters of an unstable first-order plus dead time transfer function when a limit cycle exists. This article deals with unstable processes with large time delay where the relay test is not applicable. For these processes, the conventional relay method does not induce a stable limit cycle at the output. A method to overcome the problems with inducing a sustained limit cycle output is discussed by deriving a suitable stabilizer for a feedback control. Then, a non-iterative estimation technique is given to identify the unknown parameters of a first-order mathematical model.