Power system performance is affected by transient phenomena such as different faults on power cables and transmission lines. Detection/location of the faults has great importance in order to be able to clear the fault as soon as possible and provide more reliable service to power customers. When a fault location scheme is utilized for this purpose, which uses the velocity of the propagation as a parameter during analysis, changing parameters of the transmission medium introduces large errors in determination of fault locations. The reason for the introduced error is that the travelling distance is calculated by using the travelling time and the velocity of the propagation. However, in order to have accurate fault localization, the successful analysis should not use the velocity of propagation in computer based relaying. Another important thing is that single end measurement has advantages over double end measurements. In this context, a new scheme has been developed which describes the use of wavelet analysis for identification and location of line faults without using the velocity of propagation and utilizing only one end recording. Extensive simulation work has been performed in order to confirm the effectiveness of the proposed scheme based on wavelet analysis. The obtained results indicate that the proposed scheme is effective and able to locate the points of faults with reasonable accuracy. This scheme can also be further used for the travelling wave protection on power cables for the fast and accurate fault clearance.