In this paper, we propose a network non-orthogonal multiple access (N-NOMA) technique for the downlink coordinated multipoint (CoMP) communication scenario of a cellular network, with randomly deployed users. In the considered N-NOMA scheme, superposition coding (SC) is employed to serve cell-edge users as well as users close to base stations (BSs) simultaneously, and distributed analog beamforming by the BSs to meet the cell-edge user's quality of service (QoS) requirements. The combination of SC and distributed analog beamforming significantly complicates the expressions for the signal-to-interference-plus-noise ratio (SINR) at the reveiver, which makes the performance analysis particularly challenging. However, by using rational approximations, insightful analytical results are obtained in order to characterize the outage performance of the considered N-NOMA scheme. Computer simulation results are provided to show the superior performance of the proposed scheme as well as to demonstrate the accuracy of the analytical results.