This paper proposes and analyses the power allocation coefficient normalization for successive interference cancellation in power-domain non-orthogonal multiple access. The investigation considers a single base-station transmits multiple superimposed information to mobile terminal by using the power-domain non-orthogonal multiple access strategy. Differently from the successive interference cancellation, new strategy normalizes only the designated information's power allocation coefficient by using its own power coefficient and subtracts it from the total received signal. The aforementioned process follows the order of decoding and repeats until the last information's decoding. Intensive computer simulations are in an agreement with analytical and asymptotic expressions and the obtained results reveal that the normalization strategy achieves significant coding gain on the non-normalized successive interference cancellation decoding.