Unique word (UW) OFDM is a multicarrier technique that follows a different approach than standard multicarrier techniques like cyclic prefix (CP) OFDM. It has been reported that UW-OFDM outperforms CP-OFDM in the sense that it performs better in fading channels [1, 2], and it has much lower out-of-band radiation [3] compared to CP-OFDM. However, a theoretical analysis of the error rate performance of UW-OFDM was never addressed in the literature. In this paper, we derive analytical expressions for the bit error rate for UW-OFDM, from which we can obtain the diversity order. It turns out that when the code generator matrix, needed to construct the UW-OFDM signal, is full rank, the UW-OFDM system reaches the maximum diversity order. This is in contrast with standard CP-OFDM, where only diversity order one can be reached, unless additional precoding is applied. Further, in the paper, we propose a construction method for the code generator matrix to achieve a (close to) maximum coding gain.