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In this letter, we propose a cooperative relaying system (CRS) based on non-orthogonal multiple access (NOMA) which uses an amplify-and-forward relay. This letter proposes a novel detection scheme in which the received signals of two consecutive time slots at destination is applied. We calculate asymptotic outage probability and derive diversity order of two for each symbol. Simulations show that our system has much better outage performance than NOMA-based CRS with decode-and-forward (DF) relay. Also, asymptotic ergodic sum rate increases log-linearly with transmit SNR and outperforms NOMA-based CRS with DF relay and conventional CRS. Finally, we verify analytical results by Monte-Carlo simulations.