Non-orthogonal multiple access (NOMA) is a key to multiple access techniques for the next generation 5G wireless communication networks. In this paper, to improve the performance gain of NOMA system, a cooperative fixed decode-and-forward (DF) relay system model based on NOMA (CRS-NOMA) is studied over Rician fading channels, considering the achievable rate of signals as the performance metric. In this technique, by exploiting the concept of NOMA, unlike the conventional method of cooperative relaying, the second time slot is also utilized for the realization of information sent from the transmitter end. Moreover, as the data symbols are transmitted by nodes with full power, the compulsion of complex power allocation coefficients is precluded. In conventional cooperative relaying systems, the receiver is only able to receive a single bit of information, while the receiver can reliably bring in two data symbols in two-time slots. In this regard, this scheme is able to acquire higher achievable rate performance than existing cooperative relaying schemes for larger channel powers over most of the transmit SNR regime. Furthermore, a mathematical expression is also derived for the total achievable rate of CRS-NOMA. The results are verified through Monte-Carlo simulations which validate accuracy and consistency of the derived analytical results.