The transient characteristic propagates to both ends of line from fault point when a fault occurs in the distribution networks. A determined mathematical relationship is obtained between characteristic frequencies and distance from the fault point to observation point. The identification of wave front is unnecessary when using transient signal analysis based on characteristic frequencies, so that fault location error is avoided due to waveform distortion of time domain analysis. Some achievements and shortcomings are summarized from former papers, and a new single-ended fault location method is proposed and applied to medium distribution networks, which improves signal frequencies resolution and fault location accuracy. The proposed procedure builds an fault-waveform-inferred mother wavelets firstly, which enhances the adaptability of mother wavelets and resolution of characteristic frequencies; then characteristic frequencies are corrected by scalogram in time domain based on determined frequencies on the former step. Many simulations show the new method has good adaptability and high fault location accuracy.