In this paper, a new damage-detection method based on structural vibration is proposed. The essence of the proposed method is the detection of abrupt changes in rotation. Damage-induced rotation (DIR), which is determined from the modal flexibility of the structure, initially occurs only at a specific damaged location. Therefore, damage can be localized by evaluating abrupt changes in rotation. We conducted numerical simulations of two damage scenarios using a 10-story cantilever-type building model. Measurement noise was also considered in the simulation. We compared the sensitivity of the proposed method to localize damage to that of two conventional modal-flexibility-based damage-detection methods, i.e., uniform load surface (ULS) and ULS curvature. The proposed method was able to localize damage in both damage scenarios for cantilever structures, but the conventional methods could not.