A high speed digital distance relaying algorithm based on a Wavelet Transformation is proposed. To obtain stable phasor values very quickly, first, a lowpass filter which has low cutoff frequency is used. Secondly, db2(Daubechies 2) Wavelet which has the data window of 4 samples is used. A FIR filter which removes the DC-offset component in current relaying signals is applied. In accordance with a series of tests, the operation time of the relaying algorithm is less than 3/4 cycles after faults in a 80 [km], 154[kV], 60[Hz] over-head transmission line system.