Studies have shown that when humans search for a known target, eye movements are often guided towards target features (e.g., Findlay, 1997) with occasional fixational compensations for inhomogeneous processing across the visual field (Najemnik & Giesler, 2005). In a different type of search (oddity search), targets and distractors are not known beforehand and observers have to determine whether an element in the display differs from others (distractors) along some feature. Previous research has shown that oddity search has different behavioral properties from target known search, such as different effects of set-size (Bravo & Nakayama, 1992; Schoonveld et al., 2007). Here, we measure human saccadic eye movements during an oddity search task and develop an optimal foveated oddity searcher, which fixates locations that maximize search accuracy, to evaluate human eye movement strategies. Observers performed a yes/no search task in which they were to determine whether one of the five potential target locations contained a singleton target. Stimuli consisted of Gabor patches at three orientations (5° left, vertical, 5° right) embedded in white noise at five locations around an imaginary circle (6° radius). For target present trials, the target was randomly selected from the three possible elements, while one of the remaining elements occupied the other four locations (distractors). For target absent trials, all five locations contained the same randomly selected element. Participants viewed each stimulus for 700 ms (allowing approximately three eye movements) before making a decision. Unlike typical strategies for target known search, observers adopted an eye movement strategy for the oddity search in which they systematically fixated three locations regardless of the stimulus configuration. Such strategy shows little guidance towards the target location. We find that the optimal foveated oddity searcher, like humans, seeks to survey as many of the potential target locations as possible and shows little target guidance.