Animal groups such as fish schools, bird flocks and insect swarms appear to move so synchronously that they have long been considered egalitarian, leaderless units. In schooling fish, video observations of their spatial-temporal organization have, however, shown that anti-predator manoeuvres are not perfectly synchronous and that individuals have spatial preferences within the school. Nonetheless, when facing life-or-death situations, it is not known whether schooling fish react to a threat following a random or a hierarchically-based order. Using high-speed video analysis, here we show that schooling fish (Golden grey mullet, Liza aurata) evade a threat in a non-random order, therefore individuals that are first or last to react tend to do so repeatedly over sequential stimulations. Furthermore, startle order is strongly correlated with individual positional preferences. Because school members are known to follow individuals that initiate a manoeuvre, early responders are likely to exert the strongest influence on the escape strategy of the whole school. Our results present new evidence of the intrinsic heterogeneity among school members and provide new rules governing the collective motion of gregarious animals under predator attack.