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This paper proposes a novel adaptive relaying scheme based on phasor-measurement units (PMUs) for transmission lines. The proposed adaptive relaying scheme can provide an extremely accurate discrimination between in-zone and out-of-zone faults. Two novel and composite fault discrimination indices in terms of Clarke components of synchronized voltage and current phasors at two ends of a line are derived. A line parameter estimation algorithm is developed and built in the newly designed relay to solve the uncertainty problem of line parameters. The proposed relaying scheme is independent of fault types, fault locations, fault path resistance, fault inception angles, and the variations of source impedance. The tripping decision time of the designed relay is very fast and almost held well within 6 ms for most fault events. All of the EMTP simulation results show that the proposed adaptive relaying scheme provides a high level of dependability and security.