Abstract—A new design of non-orthogonal multiple access (NOMA) is explored in this study under secrecy outage probability performance considerations. In particular, the Amplify-and-Forward (AF) relaying scheme is applied in this system model. In case of existence of an external eavesdropper, a transmitter sends confidential messages to far users in concerned NOMA system. To highlight performance of NOMA system model, orthogonal multiple access (OMA) is compared with respect to tradeoff between secure performances and transmit SNR. As important observation, the secrecy outage probability is evaluated as the secrecy metric to limit impacts of the practical passive eavesdropper in real scenario. It is confirmed that the secrecy outage is significant lower than OMA due to related parameters characterization in NOMA, and it should be controlled by varying related coefficients. Finally, we show the both of NOMA and OMA against to impact of eavesdropper in the studied problems in terms of analytically result and numerically result.