Unique word-(UW-) orthogonal frequency division multiplexing (OFDM) is a new multicarrier technique that is shown to be superior to the cyclic prefix-(CP-) OFDM system in terms of bit-error-rate performance in fading channels. Furthermore, in the literature, it is shown by simulations that UW-OFDM has a considerably lower out-of-band (OOB) radiation compared with CP-OFDM. In this paper, we derive an analytical expression to investigate the spectral characteristics of UW-OFDM to be able to determine the effect of the different system parameters on the OOB radiation. In addition, we include in our analysis the effects of the interpolation filter and the unique word. We show that the OOB radiation in UW-OFDM is mainly determined by the number of non-modulated subcarriers reserved as the guard band, and the ratio of the UW sequence length to the number of subcarriers. By increasing either of these two parameters, we show that we can suppress the OOB radiation to any amount. This is an important advantage of UW-OFDM over classic CP-OFDM systems, and shows that UW-OFDM is an excellent candidate for cognitive radio systems.