Non-orthogonal multiple access(NOMA)-based co-operative relaying system (CRS) has emerged as a solution to the spectral inefficiency problem of the conventional CRS thanks to the NOMA integration. Thus, as a subset of the NOMA-CRS, the NOMA-based diamond relaying network (NOMA-DRN) also provides a performance gain in terms of throughput. However, the NOMA-DRN has a poor error performance due to the second phase(uplink), indeed, it has an error floor regardless of the transmit power, power allocation and channel qualities. To address this problem, in this paper, we propose a novel NOMA-DRN scheme where a joint maximum likelihood(JML) decoding is implemented at the destination. Then, we define the performance metrics (i.e., bit error rate(BER) and the diversity order) of the NOMA-DRN with the JML and analyze the computational complexity. Moreover, we demonstrate that the new NOMA-DRN with JML can cope with the error floor penalty of the conventional NOMA-DRN. Hence, a spectral efficient NOMA-CRS scheme can be achieved with high data reliability. Specifically, this improvement can reach to similar to 20 - 30dB in the transmit power which is superb gain in terms of energy efficiency perspective. Furthermore, with the proposed NOMA-DRN with the JML, the full diversity order can be achieved in the low-medium SNR region.