A novel algorithm to fault detection and classification of transmission lines is proposed, by means of the wavelet singular entropy (WSE) technique. Moreover, the Euclidean Norm based on the WSE information of all phases is used to classify the faults. High frequency information plays an important role in the new "Transient Based Protection" (TBS) protection schemes, which use only the transient information of the phenomenon. Current signals are processed with the discrete wavelet transform (DWT), so that the produced energy by the wavelet coefficients is analyzed and a WSE threshold is also proposed. Fault simulation is carried out in DIgSILENT Power Factory, for phase to ground and three phase faults, for several cases of fault impedance conditions. Results shown that a time window of 5 ms is enough to identified a single-phase fault from a three-phase fault instead of the commonly 16.66 ms trip-time. The proposed algorithm shows satisfactory accuracy, and will be very useful in the TBS protection scheme for electrical power transmission systems.