In this paper, we propose an opportunistic matrix precoding algorithm for non-separable wireless MIMO-NOMA networks. It is known that NOMA is beneficial when the difference between two channel gains is very large and therefore the two channels are separable. We study general wireless MIMO-NOMA networks in which the two channels might be non-separable. Based on channel state information, we formulate and solve a non-convex optimization problem in order to maximize the sum rate and provide guaranteed rate to the weaker user. We divide the non-convex optimization problem into two parts and propose algorithms for solving them. Our simulation results show that the proposed algorithm could significantly increase the sum rate for non-separable wireless MIMO- NOMA networks in comparison with a number of alternative approaches.