Non-orthogonal multiple access (NOMA) is a candidate technology for the 5th generation cellular networks to reduce the big gap between network capacity and fast growing traffic. It applies superposition coding in transmitters and successive interference cancellation at the receivers to cancel intra-cell interference. The same frequency resource can be allocated simultaneously to multiple intra-cell users, holding large potentials on improving network performance. A major technical challenge of NOMA is on user pairing and power allocation (UPPA). Most of existing UPPA algorithms are based on exhaustive search with extensive computation. A new algorithm, which has the lowest computation complexity achievable for NOMA UPPA is proposed. The main idea is to pair the first users having the highest proportional fairness priority coefficient with potential second users having the highest channel conditions. A fixed power allocation strategy is adopted. The proposed algorithm is significantly faster than existing algorithms without sacrificing NOMA throughput gain.