Non-orthogonal multiple access (NOMA) enables multiple mobile devices to share the same frequency band. In a conventional NOMA scheme, the receiver of a far user detects its desired signal without canceling the signal for a near user. However, the signal for the near user acts as interference and degrades the accuracy of likelihood values for the far user. In this paper, a joint maximum likelihood detection scheme for the far user of the NOMA downlink is proposed. The proposed scheme takes the interference signal into account in calculating the likelihood values. Numerical results obtained through computer simulation show that the proposed scheme improves the performance by from 0.2dB to 3.1dB for power allocation coefficients of 0.2 to 0.4 at a bit error rate (BER) of 10-2 relative to the conventional scheme.