Humans involved in cooperative interactions willingly pay a cost to punish cheats. However, the proximate motives underpinning punitive behaviour are currently debated. Individuals who interact with cheats experience losses, but they also experience lower payoffs than the cheating partner. Thus, the negative emotions that trigger punishment may stem from a desire to reciprocate losses or from inequity aversion. Previous studies have not disentangled these possibilities. Here, we use an experimental approach to ask whether punishment is motivated by inequity aversion or by a desire for reciprocity. We show that humans punish cheats only when cheating produces disadvantageous inequity, while there is no evidence for reciprocity. This finding challenges the notion that punishment is motivated by a simple desire to reciprocally harm cheats and shows that victims compare their own payoffs with those of partners when making punishment decisions.