In real-time binaural rendering (or auralization), it is important to ensure that no artifacts that may result from CPU overload are heard by the listener. The research is based on the work of A. Lindau. The author states that human cannot detect a difference between signals processed with different HRTFs that represent less than 3 degrees of head position change. The method proposed performs pre-filtering and prepares three variants of the auralized signal: one corresponding to the current position of the listener's head and other two required when the head rotates more than 3 degrees to either side. The right signal can be played immediately. This method allows reducing the size of HRTF database, computation time and saving CPU labor.