After whole body rotations around an earth-vertical axis in darkness, subjects can indicate their orientation in space with respect to their initial orientation reasonably well. This is possible, because the brain is able to mathematically integrate self-velocity information provided by the vestibular system to obtain self-orientation. This process is called path integration. For rotations around multiple axes, however, computations are more demanding to accurately update self-orientation with respect to space. In such a case, simple integration is no longer sufficient due to the non-commutativity of rotations. We investigated whether such updating is possible after three-dimensional whole body rotations, and whether the non-commutativity of three-dimensional rotations is taken into account. The ability of ten subjects to indicate their spatial orientation in the earth-horizontal plane was tested after different rotational paths from upright to supine positions. Initial and final orientation of the subjects were the same in all cases, but the paths taken were different, and so were the angular velocities sensed by the vestibular system. The results show that seven of the ten subjects could consistently indicate their final orientation within the earth-horizontal plane. Thus, perceived final orientation was independent of the path taken, i.e., the non-commutativity of rotations was taken into account.