This study aims to mathematically verify the final defence positions at which the goalkeeper divides the defence range into half. The most efficient moving line strategy for goalkeeping was proposed, thereby providing basic data for goalkeeping. First, the erroneous claim from existing handball literature that handball goalkeepers should defend at the centre of the goal line and the extension of the ball was mathematically proven. Second, the final defence positions where the goalkeeper can defend at the centre of the defensive range were mathematically verified. Third, the final defence positions of the goalkeeper when shots are made from positions 6 and 9 m away from the outermost goalpost were calculated. Fourth, the positions of 231 shootings that occurred in actual game situations and the defence positions of the goalkeeper based on each shooting were compared with the mathematically verified final defence positions. Consequently, the goalkeeper's efficient positioning strategy was presented through the comparison. An error in the goalkeeper's defensive position suggested in the existing textbook was verified. This study proposed a goalkeeper's movement line that is more efficient than the semicircular movement line that was previously presented.