Forest fires are among the biggest threats to forest ecosystems and forest resources, and can lead to ecological disasters and social crises. Therefore, it is imperative to detect and extinguish forest fires in time to reduce their negative impacts. Satellite remote sensing, especially meteorological satellites, has been a useful tool for forest-fire detection and monitoring because of its high temporal resolution over large areas. Researchers monitor forest fires directly at pixel level, which usually presents a mixture of forest and fire, but the low spatial resolution of such mixed pixels cannot accurately locate the exact position of the fire, and the optimal time window for fire suppression can thus be missed. In order to improve the positioning accuracy of the origin of forest fire (OriFF), we proposed a mixed-pixel unmixing integrated with pixel-swapping algorithm (MPU-PSA) model to monitor the OriFFs in time. We then applied the model to the Japanese Himawari-8 Geostationary Meteorological Satellite data to obtain forest-fire products at subpixel level. In this study, the ground truth data were provided by the Department of Emergency Management of Hunan Province, China. To validate the positioning accuracy of MPU-PSA for OriFFs, we applied the model to the Himawari-8 satellite data and then compared the derived fire results with fifteen reference forest-fire events that occurred in Hunan Province, China. The results show that the extracted forest-fire locations using the proposed method, referred to as forest fire locations at subpixel (FFLS) level, were far closer to the actual OriFFs than those from the modified Himawari-8 Wild Fire Product (M-HWFP). This improvement will help to reduce false fire claims in the Himawari-8 Wild Fire Product (HWFP). We conducted a comparative study of M-HWFP and FFLS products using three accuracy-evaluation indexes, i.e., Euclidean distance, RMSE, and MAE. The mean distances between M-HWFP fire locations and OriFFs and between FFLS fire locations and OriFFs were 3362.21 m and 1294.00 m, respectively. The mean RMSEs of the M-HWFP and FFLS products are 1225.52 m and 474.93 m, respectively. The mean MAEs of the M-HWFP and FFLS products are 992.12 m and 387.13 m, respectively. We concluded that the newly proposed MPU-PSA method can extract forest-fire locations at subpixel level, providing higher positioning accuracy of forest fires for their suppression.