In this paper, we propose a new suboptimal antenna selection (AS) algorithm, majority based transmit antenna selection (TAS-maj), to maximize the system performance of the non-orthogonal multiple access (NOMA). The TAS-maj scheme chooses the transmit antenna with the majority. It has remarkable advantages over previously proposed AS algorithms. It has lower computational complexity than optimal AS scheme. Also, it provides better performance than the suboptimal AS algorithms, max-max-max (A³) and max-min-max (AIA), since these algorithms aim to maximize the performance of the strong and weak users, respectively. On the other hand, the TAS-maj scheme aims to optimize the performance of more than half of the mobile users in the NOMA network. In this paper, multiple-input multiple-output communication system is considered, in which all the nodes are equipped with multi-antenna. The diversity schemes TAS-maj and maximal ratio combining (MRC) are employed at the base station and mobile users, respectively. Meanwhile, the expression of the signal-to-interference-and-noise is derived. Then, the outage behavior of the NOMA with the TAS-maj/MRC scheme is investigated over Rayleigh fading channels by the Monte Carlo simulations.