Unique word (UW)-OFDM is a newly proposed multicarrier technique that has shown to outperform cyclic prefix (CP)-OFDM in fading channels. Until now, the spectrum of UW-OFDM is not thoroughly investigated. In this paper, we derive an analytical expression for the spectrum taking into account the DFT based implementation of the system. Simulations show that the proposed analytical results are very accurate. Compared to CP-OFDM, we show that UW-OFDM has much lower out-of-band (OOB) radiation, which makes it suitable for systems with strict spectral masks, as e. g. cognitive radios. Further, in this paper, we evaluate the effect of the redundant carrier placement on the spectrum.