In this paper, a transmit antenna selection (TAS) scheme is proposed for two-user downlink non-orthogonal multiple access (NOMA) network, which improves sum rate by considering the fairness between users. The proposed TAS-NOMA scheme is composed of two stages: In the first stage, base station choses k transmit antennas among its N-t antennas corresponding to k largest sum rates. In the second stage, fairness is calculated for k chosen antennas and one of them providing the maximum fairness is selected. Hence, a transmit antenna is selected in a fairer way while improving sum rate of the network. Setting k to 1 gives maximum sum rate and minimum fairness while k = N-t yields maximum fairness and degrades the sum rate. Moreover, power allocation factors must be carefully adjusted in NOMA to perform successive interference cancellation successfully. Otherwise error propagation occurs which degrades the error performance. In this paper, a power allocation technique fixing the difference between power allocation factors is adopted, which maximizes sum rate while considering the far user's rate requirement Numerical results show the performance of the proposed TAS-NOMA scheme with respect to the trade-off between fairness and sum rate in terms of k and the difference threshold between power allocation factors.