This article presents a novel approach for adaptive single-pole autoreclosing of power transmission lines under transient single-phase fault conditions by using a wavelet packet transform. In the proposed method, the mode current (sum of the currents of the two healthy phases) is captured with a sampling rate of 10 kHz and de-noised using the db8 wavelet packet to obtain signals with higher signal-tonoise ratio. The db8 wavelet packet is then used to decompose the mode current signal to attain the coefficients of wavelet nodes 131, 133, 134, 136, 137, 139, and 140 and to define an index, which is the sum of the absolute values of these node coefficients. The index is used to distinguish transient (arcing) faults from permanent faults and also to identify the secondary arc extinction instant. The proposed method has been successfully tested under a variety of fault conditions on a 500-kV overhead line using electromagnetic transient program. The test results validate the algorithm ability in distinguishing between transient and permanent faults and determining the instant of secondary arc extinction. The significant advantage of the proposed algorithm is that it does not need a case-based threshold level, and therefore, its performance is independent of fault location, line parameters, and pre-fault line loading conditions. Moreover, the algorithm can be used in transmission lines with reactor compensation.