During faults, the voltage and current signals available to the relay are affected by the decaying dc component and harmonics. In order to make appropriate and accurate decisions, most of the relaying algorithms require the fundamental frequency phasor information that is immune to decaying dc effect and harmonics. The conventional Fourier ph as or estimation algorithm is affected by the presence of decaying-exponential transients in the fault signal. This paper presents a modified Fourier algorithm, which effectively eliminates the decaying dc component and the harmonics present in the fault signal. The decaying dc parameters are estimated by means of an out-of-band filtering technique. The decaying dc offset and harmonics are removed by means of a simple computational procedure that involves the design of two sets of Orthogonal digital OFT filters tuned at different frequencies and by creating three off-line look-up tables. The technique was tested for different decay rates of the decaying dc component. It was also compared with the conventional mimic plus the full cycle OFT algorithm. The results indicate that the proposed technique has a faster convergence to the desired value compared to the conventional mimic plus OFT algorithms over a wide range of decay rates. In all cases, the convergence to the desired value was achieved within one cycle of the power system frequency.