This work considers the exact bit error rate (BER) analysis of a two-user non-orthogonal multiple access (NOMA) system using quadrature amplitude modulation (QAM). Unlike existing work, no constraints on the modulation order of the QAM symbols for any user. Closed-form expressions are derived for the BER of joint multiuser detector (JMuD), which is demonstrated that it is equivalent to the successive interference cancellation (SIC) receiver. Moreover, a general expression is derived for the relation between the power allocation factors for the two users, which depends on the modulation order for each user.