Due to the large field angle and large geometric distortions of the HaiYang-1C ultraviolet imager (UVI), a single rational function model (SRFM) is unable to fully absorb the geometric distortions. The SRFM-based sensor orientation accuracy of the UVI images is thereby worse than expected. In order to improve the sensor orientation accuracy, a feasible sensor orientation method for the UVI images based on a piecewise rational function model (PRFM) is proposed. A complete UVI image is first logistically divided into five subimages, and the adjacent subimages have an overlap. Then, an SRFM is used to mathematically fit the physical sensor model of each subimage. Finally, the five SRFMs form a continuous PRFM, and the PRFM-based sensor orientation of the UVI images is performed. Three HaiYang-1C UVI images were tested. The experimental results showed that the unabsorbed geometric distortions fully propagated into the SRFM-based sensor orientation results. The orientation accuracy of the three images reached ∼7  pixels. In the PRFM-based sensor orientation, both the PRFM fitting errors and the inconsistent errors between the adjacent subimages could be negligible. The PRFM-based orientation accuracy was thereby noticeably improved and reached >1  pixel.