In this paper, we propose a new detection algorithm for single carrier-frequency division multiple access (SC-FDMA) systems called duo maximum likelihood detector with transmit power allocation (DMLD-TPA). The proposed scheme is based on iteratively detecting two symbols out of Q transmit symbols by an orthogonal projection. It can make the detection complexity less than that of the maximum likelihood detector (MLD). In addition, we also propose a transmit power allocation scheme without the channel information feedback to enhance the BER performance. As a result, DMLD-TPA can keep the complexity low and its BER performance approaches that of the MLD.