A coordinated direct and relay transmission is proposed using uplink non-orthogonal multiple access (UP-NOMA). A two-user UP-NOMA scenario is considered, where a cell-center user directly communicates with a base station (BS), whereas a cell-edge user needs the assistance of a half-duplex decode-and-forward relay to communicate with the BS. The ergodic sum capacity of UP-NOMA is analyzed under both perfect and imperfect successive interference cancellation. The superiority of UP-NOMA over conventional multiple access is demonstrated through simulation and analysis.