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Recently, development of a numerical calculation of the head-related transfer function (HRTF) has been conducted using a computer model of a human head and the boundary element method. The reciprocity theorem is incorporated into the computational process in order to shorten the computational time, which is otherwise very long. On the other hand, another fast HRTF calculation method for any source position, which is realized by calculating factors independent of the source position in advance, has been suggested by the authors. Using this algorithm, the HRTF for any source position can be obtained in a few seconds with a common PC. The resulting HRTFs are more precise and are calculated faster than those by using the reciprocity theorem. However, speeding the process up even further is required in order to respond to a head movement and rotation or to moving sources during binaural sound reproduction. In this paper, a faster calculation method by incorporating a time domain operation into the authors’ previous algorithm is proposed. Additionally, the new formulation, which eliminates the extra computational time in the preprocess, is proposed. This method is shown to be faster than the previous ones, but there are some discrepancies at higher frequencies. [ABSTRACT FROM AUTHOR]