Single carrier cyclic prefix system with frequency domain equalization (SC-CP-FDE) is an attractive technology for broadband wireless communications. In this paper, we investigate the diversity order of a SC-CP-FDE system without channel coding in frequency-selective channels. Existing analytic proofs in [6], [7] indicate that the achievable diversity order is only 1, which contradicts the conclusion in [11] and simulation results in [1]-[3]. We explain why the proofs in [6], [7] can not support the claim that SC-CP system is unable to provide any frequency diversity gain. We then re-investigate the diversity order of a SC-CP system with frequency domain decision feedback equalizer (FD-DFE) based on MMSE criteria at the receiver end. Adopting outage analysis instead of pairwise error probability (PEP) analysis, we show that with MMSE-FD-DFE, the asymptotic achievable diversity order is Lc +1 when the block length N is sufficiently large, where Lc +1 is the number of independent channel paths, i.e., full multipath diversity is asymptotically achieved.