A self-centering damper has an elongated damping body and at least one returning device. The elongated damping body has at least one first wing plate and a supporting element connected to and extending from the first wing plate. The at least one returning device is connected to the damping body and has two holding rib plates respectively connected to the end segments of the damping body, a supporting rib plate securely connected to the damping body between the holding rib plates and at least one pre-stressed stay wire extending through the supporting rib plate and connected the holding rib plates in a tension condition.