Animals can exhibit complex movement patterns that may be the result of interactions with their environment or may be directly the mechanism by which their behaviour is governed. In order to understand the drivers of these patterns we examine the movement behaviour of individual desert locusts in a homogenous experimental arena with minimal external cues. Locust motion is intermittent and we reveal that as pauses become longer, the probability that a locust changes direction from its previous direction of travel increases. Long pauses (of greater than 100 s) can be considered reorientation bouts, while shorter pauses (of less than 6 s) appear to act as periods of resting between displacements. We observe power-law behaviour in the distribution of move and pause lengths of over 1.5 orders of magnitude. While Lévy features do exist, locusts' movement patterns are more fully described by considering moves, pauses and turns in combination. Further analysis reveals that these combinations give rise to two behavioural modes that are organized in time: local search behaviour (long exploratory pauses with short moves) and relocation behaviour (long displacement moves with shorter resting pauses). These findings offer a new perspective on how complex animal movement patterns emerge in nature.