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We investigate a relay network where the source can potentially utilize an untrusted non-regenerative relay to augment its direct transmission of a confidential message to the destination. Since the relay is untrusted, it is desirable to protect the confidential data from it while simultaneously making use of it to increase the reliability of the transmission. We first examine the secrecy outage probability (SOP) of the network assuming a single antenna relay, and calculate the exact SOP for three different schemes: direct transmission without using the relay, conventional non-regenerative relaying, and cooperative jamming by the destination. Subsequently, we conduct an asymptotic analysis of the SOPs to determine the optimal policies in different operating regimes. We then generalize to the multi-antenna relay case and investigate the impact of the number of relay antennas on the secrecy performance. Finally, we study a scenario where the relay has only a single RF chain which necessitates an antenna selection scheme, and we show that unlike the case where all antennas are used, under certain conditions the cooperative jamming scheme with antenna selection provides a diversity advantage for the receiver. Numerical results are presented to verify the theoretical predictions of the preferred transmission policies.