Non-orthogonal multiple access (NOMA)-based cooperative relaying systems (CRS) are very promising to overcome spectral inefficiency of conventional cooperative communications. Although NOMA-CRS have great recent attention, almost all studies investigate NOMA-CRS only in terms of capacity and outage probability. Error performances of NOMA-CRS have not been well-studied. In this paper, we analyze error performance of NOMA-based diamond relaying network (NOMA-DRN) with imperfect successive interference canceler (SIC) as a NOMA-CRS scheme. We derive exact bit error probability (BEP) for NOMA-DRN and provide a tight approximated BEP in the closed-form. In addition, high-SNR analysis is conducted to present that NOMA-DRN has an error floor. Moreover, it is proved that NOMA-DRN turns out to be a non-equiprobable communication system and we derive priori probabilities of symbols. All derived expressions are validated via computer simulations.