This letter proposes a novel hybrid half-/full-duplex relaying scheme to enhance the relay channel security. A source node (Alice) communicates with her destination node (Bob) in the presence of a buffer-aided full-duplex relay node (Rooney) and a potential eavesdropper (Eve). Rooney adopts two different relaying, namely randomize-and-forward and decode-andforward relaying strategies, to improve the security of the legitimate system. In the first relaying strategy, Rooney uses a codebook different from that used at Alice. In the second relaying strategy, Rooney and Alice use the same codebooks. In addition, Rooney switches between half-duplex and full-duplex modes to further enhance the security of the legitimate system. The numerical results demonstrate that our proposed scheme achieves a significant average secrecy end-to-end throughput improvement relative to the conventional bufferless full-duplex relaying scheme.