This paper sought to improve the precision of the Alternating Current Electro-Occulo-Graphy (AC-EOG) gaze estimation method. The method consisted of two core techniques: To estimate eyeball movement from EOG signals and to convert signals from the eyeball movement to the gaze position. In conventional research, the estimations are computed with two EOG signals corresponding to vertical and horizontal movements. The conversion is based on the affine transformation and those parameters are computed with 24-point gazing data at the calibration. However, the transformation is not applied to all the 24-point gazing data, but to four spatially separated data (Quadrant method), and each result has different characteristics. Thus, we proposed the conversion method for 24-point gazing data at the same time: To assume an imaginary center (i.e., 25th point) on gaze coordinates with 24-point gazing data and apply an affine transformation to 24-point gazing data. Then, we conducted a comparative investigation between the conventional method and the proposed method. From the results, the average eye angle error for the cross-shaped electrode attachment is x = 2.27 ° ± 0.46 ° and y = 1.83 ° ± 0.34 ° . In contrast, for the plus-shaped electrode attachment, the average eye angle error is is x = 0.94 ° ± 0.19 ° and y = 1.48 ° ± 0.27 ° . We concluded that the proposed method offers a simpler and more precise EOG gaze estimation than the conventional method.