Here we investigate the counting ability in honeybees by training them to receive a food reward after they have passed a specific number of landmarks. The distance to the food reward is varied frequently and randomly, whilst keeping the number of intervening landmarks constant. Thus, the bees cannot identify the food reward in terms of its distance from the hive. We find that bees can count up to four objects, when they are encountered sequentially during flight. Furthermore, bees trained in this way are able count novel objects, which they have never previously encountered, thus demonstrating that they are capable of object-independent counting. A further experiment reveals that the counting ability that the bees display in our experiments is primarily sequential in nature. It appears that bees can navigate to food sources by maintaining a running count of prominent landmarks that are passed en route, provided this number does not exceed four.