In this work, non-orthogonal multiple access (NOMA) in coordinated direct and relay transmission (CDRT) is introduced, where a base station (BS) directly communicates with user equipment 1 (UE1) while communicating with user equipment 2 (UE2) only through a relay. The main challenge of nonorthogonal CDRT can be solved by using the inherent property of NOMA that allows a receiver to obtain side information such as other TIE's data for interference cancellation. Analytical expressions for outage probability and ergodic sum capacity are provided. It is shown that the proposed NOMA in CDRT provides remarkable performance gain compared with NOMA in non-coordinated direct and relay transmission (nCDRT); the sum capacity scaling of the proposed scheme is log ρ_b as signal-to-noise-ratio (SNR) ρ_b increases, but 1/2log ρ_b for NOMA in nCDRT. Exact and closed-form expressions for outage probability of each stream for UE1 and UE2 are respectively derived, and it is shown that the achievable diversity orders for each stream are same as one.