In this paper, we consider an unmanned aerial vehicle (UAV)-assisted downlink cellular network consisting of a single base station (BS), two mobile stations (MSs) with N antennas, and K UAV relay stations (RSs). We assume that there exists no direct link between the BS and the MSs due to unexpected blockages such as obstacles and disasters. We propose a UAV-assisted cooperative downlink non-orthogonal multiple access (NOMA) with virtual full-duplex (VFD) operation for improving spectral efficiency in such an environment. In the proposed VFD technique, a single UAV-RS is selected among multiple UAV-RS. Through computer simulations, we verify that the proposed cooperative NOMA technique with VFD operation significantly outperforms the conventional cooperative NOMA technique with half-duplex operation in terms of outage probability. Keywords: Unmanned aerial vehicle (UAV), UAV-assisted cooperative communications, Outage probability, Non-orthogonal multiple access (NOMA), Relay selection algorithm