The bit error rate (BER) analysis of non-orthogonal multiple access (NOMA) has been widely considered in the literature with the assumptions of perfect and imperfect successive interference cancellation (SIC). For both cases, exact closed-form formulas were derived under various channel models, number of users, and modulation orders. However, all the analysis reported overlooked the transformations that affect the additive white Gaussian noise (AWGN) probability density function (PDF) after the SIC process. Therefore, the signal model after the SIC process is generally inaccurate, which makes the analysis just approximations rather than exact. The same discussion applies to the analysis with perfect SIC assumption because the noise after successful SIC is not Gaussian anymore. Therefore, this letter derives the exact noise PDF after the SIC process and evaluates its impact on the BER analysis. The analytical results obtained show that the noise PDF after SIC should be modeled as a truncated Gaussian mixture. Moreover, the PDF after successful and unsuccessful SIC should be modeled differently. Comparing the BER of the legacy perfect SIC formula and the exact one shows that the BER using the exact PDF is generally less than the Gaussian case, particularly for low signal-to-noise ratios (SNRs)and low far-user power allocation.