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While participants made 10 horizontal saccades, two dots were presented, one before and one after the saccade. Each dot was presented for 400 ms, the first turned off about 100 ms before, while the second turned on about 100 ms after the saccade. The two dots were separated vertically by 3, but because of the intervening eye movement, they were also separated horizontally on the retina by an additional 10. Participants nevertheless reported that the perceived motion was much more vertical than horizontal, suggesting that the trans-saccadic displacement was corrected, at least to some extent, for the retinal displacement caused by the eye movement. The corrections were not exact, however, showing significant biases that corresponded to about 5% of the saccade amplitude. The perceived motion between the probes was tested at 9 different locations and the biases, the deviations from accurate correction, varied significantly across locations. Two control experiments for judgments of position and of verticality of motion without eye movement confirmed that these biases are specific to the correction for the saccade. The local variations in the correction for saccades are consistent with physiological “remapping” proposals for space constancy that individually correct only a few attended targets but are not consistent with global mechanisms that predict the same correction at all locations.