A novel transceiver antenna selection (TRAS) strategy selecting a pair of antennas for transmission and reception at terminal sources for full-duplex amplify-forward multi-input multi-output two way relay networks is proposed. Antenna pair is selected in accordance with maximum and second maximum signal to self-interference-plus-noise ratio between the sources and relay, where the terminal sources and relay are full-duplex. Unlike reciprocal channel gains, forward and backward paths between the sources and relay are taken to be different. With four different antenna selection (AS) scenarios, the exact sum outage probability (SOP) for fading self-interference (SI) and the exact, approximated, and asymptotic SOP expressions for nonfading SI over Rayleigh fading channels are derived and validated via Monte Carlo simulation technique. The proposed AS strategy uses all antenna space for either transmission or reception which results in a reduction in total number of antennas at each terminal node. It is shown that performance can be significantly improved by usage of offered TRAS strategy at terminal sources. For example, up to 25 dB gain is obtained for five antennas at the sources with respect to no selection case of two antennas. In addition, it outperforms the selection strategy using maximum paths from two divided antenna sets at each source, where one set is only used for transmission and the other one for reception. The diversity order of the system is proven to be dependent on SI and varies between zero and minimum of the total number of antennas of two sources minus 1. For different SI values, optimum power allocations are demonstrated and factors affecting optimum relay location are also elaborated. Each AS scenario produces the lowest SOP for different combinations of SI occurrences, power allocations, and relay locations.