The pitch measuring accuracy for gear measuring instruments (GMIs) is evaluated by measuring a calibrated artifact. We proposed a novel artifact which called multiball artifact (MBA). The MBA is composed of the pitch balls assumed to gear teeth and the reference axis assumed to a center axis of gear. The MBA can be calibrated more accurate than a conventional pitch artifact. When the MBA is calibrated, it is important to eliminate an error of measuring instrument; therefore we calibrate the MBA adapting the multiple-orientation technique. In the multiple-orientation technique, the MBA is set up in difference orientations around the reference axis and the measurement error is eliminates by averaging the measurement value for all orientations. There are, however, Fourier components of the measurement error that can not be eliminated depending on the total number of orientations. In this paper, we propose the advanced calibration method; the error separation method for the multiple-orientation technique is improved and the total number of orientations can be reduced. The superiority of the proposed method is clarified from the calibration results using the MBA.