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In the presence of an illegitimate user, we investigate the secrecy outage probability (SOP) of the optimal relay selection (ORS) networks by applying decode-and-forward (DnF) based full-duplex (FD) relaying mode. The closed-form expressions for the allocations of the end-to-end signal-to-interference-plus-noise ratio (SINR) in each wireless network are derived as well as the closed-form expression for the exact SOP of the proposed ORS system is presented under Rayleigh fading schemes. As an important achievement, SOP is also compared between orthogonal multiple access (OMA) and non-orthogonal multiple access (NOMA) schemes. Our results reveal that the SOP of the suggested scheme can be considerably influenced by several parameters involved, including the number of relays, the average signal-to-noise ratio (SNR) of eavesdropper links, transmit power and the average residual self-interference (SI) enforced on the FD relays. DOI: http://dx.doi.org/10.5755/j01.eie.24.4.21483