In binocular rivalry, only one image is perceived consciously when different, incompatible images are presented to the left and right eye, respectively. The other image is suppressed. Binocular suppression is generally assumed to occur within retinotopic coordinates. However, the world is continuously shifting on our retina because of the movements of the eyes and the objects themselves. Therefore, the visual system needs a mechanism to create binocular perceptual stability despite continuous changes in the retinal images. To investigate retinotopic versus object-centered binocular suppression, we combined the Ternus-Pikler paradigm with a binocular selective suppression paradigm. We presented a Ternus-Pikler display (TPD) in which three disks shifted by one position from frame 1 to frame 2. We presented a low-contrast grating in the central disk of the TPD to one eye and a high contrast bull’s eye at the same location to the other eye. The bull’s eye fully suppressed the percept of the grating. In the second frame, in half of the trials, a grating was presented on the central disk. In the other half, no grating was presented. The orientation of the grating (when presented) was the same as or orthogonal to the orientation of the first grating. No bull’s eye was presented in the second frame. Sensitivity to gratings with the previously suppressed orientation was reduced compared to orthogonal gratings, even though the gratings in both frames were presented at different retinotopic locations. These results are evidence for feature suppression in non-retinotopic, object-centered coordinates, giving rise to a new view on binocular rivalry where stimulus-selective, non-retinotopic inhibition is crucial in maintaining perceptual stability.