When subjects look at a rubber hand being brush-stroked synchronously with their own hidden hand, they might feel a sense of ownership over the rubber hand. The perceived mislocalization of the own hand towards the rubber hand (proprioceptive drift) would reflect an implicit marker of this illusion occurring through the dominance of vision over proprioception. This account, however, contrasts with principles of multisensory integration whereby percepts result from a "statistical sum" of different sensory afferents. In this case, the most-known proprioceptive drift should be mirrored by complementary visual drift of the rubber hand in the opposite direction. We investigated this issue by designing two experiments in which subjects were not only requested to localize their own hand but also the rubber hand and further explored the subjective feeling of the illusion. In both experiments, we demonstrated a (visual) drift in the opposite direction of the proprioceptive drift, suggesting that both hands converge toward each other. This might suggest that the spatial representations of the two hands are integrated in a common percept placed in between them, contradicting previous accounts of substitution of the real hand by the rubber hand.