To estimate sound direction of arrival with a pair of microphones, a method based on Time Difference of Arrival (TDOA) estimation using the Cross Power Spectrum Phase (CPSP) function is largely used due to its simplicity and good performance. In this paper, we investigate CPSP maximum values for various SNRs and adverse environments, and propose a novel method to improve the estimation performance of sound direction of arrival. The proposed method applies a threshold to the CPSP values and increases the reliability of the estimated sound direction. Through computer simulation for various SNRs, we validate the effectiveness of the proposed method. When the threshold was set to 0.1, more than 90% of success rate of sound direction of arrival estimation has been achieved for directions of $10^{circ}$, $40^{circ}$, $70^{circ}$ from the source location even with reverberation times of 0.1s.