Pupillometry, thanks to its strong relationship with cognitive factors and recent advancements in measuring techniques, has become popular among cognitive or neural scientists as a tool for studying the physiological processes involved in mental or neural processes. Despite this growing popularity of pupillometry, the methodological understanding of pupillometry is limited, especially regarding potential factors that may threaten pupillary measurements' validity. Eye blinking can be a factor because it frequently occurs in a manner dependent on many cognitive components and induces a pulse-like pupillary change consisting of constriction and dilation with substantive magnitude and length. We set out to characterize the basic properties of this "blink-locked pupillary response (BPR)," including the shape and magnitude of BPR and their variability across subjects and blinks, as the first step of studying the confounding nature of eye blinking. Then, we demonstrated how the dependency of eye blinking on cognitive factors could confound, via BPR, the pupillary responses that are supposed to reflect the cognitive states of interest. By building a statistical model of how the confounding effects of eye blinking occur, we proposed a probabilistic-inference algorithm of de-confounding raw pupillary measurements and showed that the proposed algorithm selectively removed BPR and enhanced the statistical power of pupillometry experiments. Our findings call for attention to the presence and confounding nature of BPR in pupillometry. The algorithm we developed here can be used as an effective remedy for the confounding effects of BPR on pupillometry.