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This paper presents a novel directional relay based on travelling waves for transmission line protection, referred to as the surge impedance relay (SIR). It determines fault direction by the ratio of initial voltage and current travelling waves under multiple frequency bands. In order to ensure the reliability of the relay, which has been a serious problem for travelling-wave-based relays, both the polarity and amplitude of the initial wave are used. In order to extract travelling waves from post-fault voltages and currents, and to construct an effective relaying algorithm, wavelet transforms were adopted. Because the fault information under the multiple frequency bands were used in the relaying algorithm, the SIR's reliability has been further improved. Theoretical analysis and EMTP simulations verified the directional relay. Finally, the paper introduces a scheme to implement the relay.