All practical orthogonal frequency-division multiplexing (OFDM) systems require a prefix to eliminate intersymbol interference (ISI) at the receiver. Cyclic prefix (CP) and zero padding are well-known prefix construction methods, with the former being the most employed technique in practice due to its lower complexity. In this paper, we construct an OFDM system with a generalized CP. It is shown that the proposed generalized prefix effectively makes the channel experienced by the packet different from the actual channel. Using an optimization procedure, lower bit error rates (BERs) can be achieved, outperforming other prefix construction techniques. At the same time, the complexity of the technique is comparable with the CP method. The presented simulation results show that the proposed technique not only outperforms the CP method but is more robust in the presence of channel estimation errors and mobility as well. Therefore, the proposed method is appropriate for practical OFDM systems.