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In this study, the relationship between a person’s walking speed and the perception threshold for discrete implicit repositioning during eyeblinks in a virtual environment is investigated. The aim is to estimate the perception thresholds for forward and backward repositioning during forward translation following eyeblink occurrences. A psychophysical method called Staircase Transformed and Weighted up/down is utilized to quantify the perception thresholds for forward and backward repositioning. The perception thresholds for this repositioning are estimated for three different walking speeds: slow (0.58 m/s), moderate (0.86 m/s), and fast (1.1 m/s). The collected observations are then analyzed using regression analysis. The estimated perception threshold values for imperceptible forward repositioning were 0.374, 0.635, and 0.897 meters for the abovementioned walking speeds, respectively. Moreover, the respective perception threshold values for imperceptible backward repositioning were 0.287, 0.430, and 0.572 meters for the same walking speeds. The findings reveal a proportional relationship between the perception threshold values and the participant’s walking speed. As such, it is possible to imperceptibly reposition a participant at a greater distance when they are walking faster relative to the same situation when the participant is walking slower. In addition, the results show that there is more tolerance in forward discrete repositioning compared to backward discrete repositioning during forward translation. These findings enable the extension of the manipulation types utilized by the Redirected Walking Technique. More specifically, this allows for implementing a sophisticated composite redirected walking controller, which utilizes continuous and discrete translation gains simultaneously; this helps not only with reducing the cognitive load, but also with reducing the amount of physical space required to support infinite free exploration in an immersive virtual environment.