In this paper, two approaches to determining the non-zero initial conditions for the difference equation of notch filters are proposed and analyzed. The vector of non-zero initial conditions is determined to reduce the transient of the considered IIR notch filters. Both presented approaches are based on the vector projection method. The first method is based on the iterative determination of the vectors of initial conditions using samples available at a given moment. The main goal of the second approach is to reduce the computational cost compared to the first method with a slight deterioration in the quality of filtration. In order to demonstrate the suitability of the proposed methods, they have been used in simulation studies of power line interference filtering from disturbed ECG signals. The use of the proposed methods allowed for a significant reduction of the transient in the filter response with a shorter delay than in the classical vector projection method.