Flocking is a striking example of collective behaviour that is found in insect swarms, fish schools and mammal herds. A major factor in the evolution of flocking behaviour is thought to be predation, whereby larger and/or more cohesive groups are better at detecting predators (as, for example, in the 'many eyes theory'), and diluting the effects of predators (as in the 'selfish-herd theory') than are individuals in smaller and/or dispersed groups. The former theory assumes that information (passively or actively transferred) can be disseminated more effectively in larger/cohesive groups, while the latter assumes that there are spatial benefits to individuals in a large group, since individuals can alter their spatial position relative to their group-mates and any potential predator, thus reducing their predation risk. We used global positioning system (GPS) data to characterise the response of a group of 'prey' animals (a flock of sheep) to an approaching 'predator' (a herding dog). Analyses of relative sheep movement trajectories showed that sheep exhibit a strong attraction towards the centre of the flock under threat, a pattern that we could re-create using a simple model. These results support the long-standing assertion that individuals can respond to potential danger by moving towards the centre of a fleeing group.