This paper proposes a new residual carrier frequency offset (CFO) estimation technique for the unique word (UW) based single-carrier transmission with frequency domain equalizer (SC-FDE) on frequency selective channels. In extremely frequency selective channels, UW symbols for CFO estimation can also be corrupted by the inter-symbol interference (ISI). Since the UW can be included in the equalizer, we employ the FDE before the CFO estimation. Moreover, we utilize the repeated pattern of UW symbols to improve the estimation accuracy.