This paper presents a novel method of fault location. We theoretically analyze the transient waveforms caused by the faults on single-phase transmission lines above a perfectly conducting ground, and prove that they are represented by Laguerre functions. Based on the orthogonality of Laguerre functions, we propose a method of fault location by a correlation filter bank. This method can detect the faults and estimate fault points faster than the conventional method which observes the impedance of transmission lines.