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This study presents a protective algorithm for discrimination and classification of short-circuit faults in parallel circuit transmission lines. The proposed algorithm is based on the initial fault-induced current travelling waves (TWs) detected by the relay using the wavelet transform. In the case of internal faults on any of the parallel circuits, the detected current TWs in the corresponding phases of the parallel circuits are different, whereas, for external faults, the initial current TWs are almost similar. This feature is used to discriminate between internal and external faults. A fault-type classification algorithm is also proposed to identify the faulted phases. The proposed algorithm only uses the initial current TWs caused by the fault and provides an ultra-high-speed protective technique. It also covers inter-circuit faults, in which phases of both parallel circuits get involved in the fault. The obtained simulation results using the PSCAD/EMTDC software show that the proposed algorithm is able to discriminate the internal faults and to select the faulted phases very rapidly and reliably. It is able to identify faults in just ~1~ms.