Due to the ability to handle a large number of users, low latency, and high data rates, NON-orthogonal multiple access (NOMA) is considered a promising access technology for next-generation communication systems. However, as the number of users increases, each user experiences a greater number of successive interference cancellations (SIC), causing the system’s performance to decline. With the increase in the number of users, the fraction of power allocated to each user becomes smaller. Cooperative communication in downlink NOMA is considered as a potential approach to enhance the reliability, capacity, and performance over wireless channels. Space-time block code (STBC)-aided cooperative NOMA (CNOMA) offers an opportunity to improve the weak users’ signal-to-interference-plus-noise (SINR) through strong user cooperation. In this paper, we study the symbol error probability (SEP) performance of the STBC-NOMA and derive the asymptotic expression for SEP when the network is impaired with imperfect SIC (ipSIC) and timing offsets. The simulation results show that the performance of STBC-NOMA was degraded significantly with an increase in the imperfection of SIC and timing errors and that traditional orthogonal access schemes, such as orthogonal frequency division multiple access (OFDMA) and time division multiple access (TDMA), should be used after a threshold SIC level.