Autotuning based on relay feedback tests have received a great deal of attention recently. The relay feedback tests fail to generate sustained oscillation in some cases. For systems with RHP poles and/or zeroes, incorrect autotune identification procedure may give erroneous information and unstable limit cycle. Frequency domain analyses provide a criteria for prediction of the existence of stable limit cycle. Furthermore, a procedure is given to ensure the success of a relay feedback test. The analyses and procedure are illustrated through open loop stable and unstable systems. Results show that, except for some rare occasion, successful relay feedback experiments can be obtained following the proposed procedure.