This paper presents an efficient and innovative method to remove the damping DC offset from fault currents in power systems. In this method, the instantaneous value of the damped DC offset is obtained using exact integration of the input signal. After calculating this value, the DC component is effectively removed by subtracting the instantaneous DC value from the original signal at each sampling instant. After this step, Discrete Fourier Transform (DFT) is applied to the signal without offset to extract the phasor of the principal component of the fault current. This method is capable of separating transient and error signals with high accuracy. In this research, to evaluate the efficiency of the proposed method, various transient signals including single-phase and multi-phase faults have been investigated in different network conditions. The results of the simulations show that this proposed method is not only highly accurate, but its implementation is also easier and faster than other methods. These characteristics make the proposed method as a practical and effective solution for use in power protection and measurement systems. Other advantages of this method include reducing the computational complexity and improving the response time of the system, which is especially important in industrial environments and large power systems.