Flux transfer events (FTEs) are magnetic structures generally believed to originate from time-varying magnetic reconnection at the Earth’s magnetopause. Despite years of research, the mechanism of how FTEs are formed through reconnection remains controversial. In various models, FTEs exhibit different global configurations. Studying the FTE axial orientation can provide insights into their global shape, thereby helping to distinguish the generation mechanisms. In this paper, taking advantage of the orbital characteristics of the four Cluster spacecraft, we devised a multi-spacecraft timing method to determine the axes of a total of 57 FTEs observed sequentially by Cluster during a high-latitude duskside magnetopause crossing. During the nearly five-hour observation, the interplanetary magnetic field (IMF) experienced a large rotation, leading to a substantial rotation of the magnetosheath magnetic field. The analysis results show two new features of the FTE axis that have not been reported before: (1) the axes of the FTEs gradually rotate in response to the turning of the IMF and the magnetosheath magnetic field; (2) the axes of the FTEs vary between the direction of the magnetosheath magnetic field and the direction of the reconnection X-line. These features indicate that FTEs may have a more complex global configuration than depicted by traditional FTE models.