In this letter, non-regenerative Amplify-and-Forward (AF) relay systems based on half and full duplex schemes are investigated and their performance is analyzed and compared in terms of outage probability. Although the AF relay systems have been widely investigated in many previous literatures, most of them adopted a half duplex scheme due to hardware limitation and mathematical tractability. To the best of our knowledge, this letter is the first study to investigate the performance of the full duplex AF relay system considering practical hardware limitations. In full duplex AF relay systems, it is important to secure the isolation between transmit and receive antennas. Our numerical and simulation results show that there exists a threshold point of the isolation gain that the full duplex relay system outperforms the half duplex relay system.