In this paper, a non-orthogonal multiple access (NOMA) downlink scenario is considered, in which all nodes are equipped with multiple antennas. A new design of precoding and detection matrices for multiple-input-multiple-output (MIMO) downlink transmissions is proposed and its performance is analyzed by using the criteria of outage probabilities and diversity orders. To further enlarge the performance gap between MIMO-NOMA and conventional orthogonal multiple access schemes, user pairing is applied to NOMA and its impact on the system performance is characterized. Finally computer simulation results are provided to facilitate the performance evaluation of MIMO-NOMA and also demonstrate the accuracy of the developed analytical results.