In this paper, we propose a novel transmit antenna selection (TAS) scheme to improve the physical layer security of two-user non-orthogonal multiple access (NOMA) systems. Specifically, the proposed TAS scheme aims to select an antenna that is the most robust against the interception of an eavesdropper, in particular, the antenna that minimizes the maximum capacity of the eavesdropper channels. To evaluate the performance of the proposed scheme, we derive an exact closed-form expression for the secrecy outage probability (SOP) of the near user and a tight approximated closed-form expression for the SOP of the far user. Numerical results reveals that the proposed TAS scheme improves the total secrecy outage probability compared to that of some existing schemes. We also provide some insightful discussions on the impact of the number of antenna and the location of the eavesdropper on the security capability of the considered system.