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An adaptive wavelet algorithm (AWA) is presented, applied to classifying transitory events caused by faults in transmission lines. The algorithm generates the wavelets on the basis of the fundamental definitions of discrete wavelet transform (DWT) using a classification method based on probability such as the Bayesian linear discrimination analysis. A discriminant criterion shows the capacity of the method for distinguishing between fault types (classes). In order to do this, it only uses the current measurements of just one phase of the transmission line. The algorithm can be applied to high-speed transient-based protection (TBP) schemes that employ data windows shorter than one-fourth cycle of the fundamental frequency of the system. The results show a high level of success in the classification, even higher than the approach using mother wavelets pertaining to known families, such as Daubechies.