<h3>ABSTRACT</h3> To capture where things are and what they are doing, the visual system may extract the position and motion of each object relative to its surrounding frame of reference<sup>e.g.,1,2</sup>. Here we report a particularly powerful example where a paradoxical stabilization is produced by a moving frame. We first take a frame that moves left and right and we flash its right edge before, and its left edge after, the frame’s motion. For all frame displacements tested, the two edges are perceived as stabilized, with the left edge on the left and right edge on the right, separated by the frame’s width as if the frame were not moving. This illusory stabilization holds even when the frame travels farther than its width, reversing the actual spatial order of the two flashes. Despite this stabilization, the motion of the frame is still seen, albeit much reduced, and this hides the paradoxical standstill of relative positions. In a second experiment, two probes are flashed inside the frame at the <i>same</i> physical location before and after the frame moves. Despite being physically superimposed, the probes are perceived widely separated, again as if they were seen in the frame’s coordinates and the frame were stationary. This illusory separation is set by the distance of the frame’s travel, independently of its speed. This paradoxical stabilization suggests a link to visual constancy across eye movements where the displacement of the entire visual scene may act as a frame to stabilize the perception of relative locations.