One of the main characteristics of the power-domain non-orthogonal multiple access (NOMA) technique is the possibility of users to decode the messages of the other paired users on the same resources. This technique exhibits a security threat particularly if the base station (BS) have to serve untrusted users or users with different security clearance. In this paper, we study the outage probability and the secrecy outage probability in a two-users NOMA system at which the BS is pairing a legitimate/trusted user with another untrusted user due to the non-uniform distribution of trusted and untrusted users in the cell. Through the NOMA concept, we investigate the NOMA pair outage behavior under secrecy outage probability constraint on the trusted user. More specifically, the pair outage probability (OP) and the secrecy outage probability (SOP) of the trusted user are derived in closed form expressions. We provide insights on the feasibility of achieving an outage-optimal performance for the pair under the SOP constraint. Through numerical simulations, we verify the correctness of our analytical derivations under different scenarios.