Left- and right-isocliny defined as above seem to depend on which specific isoclinic rotation was selected. However, when another isoclinic rotation with its own axes , , , is selected, then one can always choose the order of , , , such that can be transformed into by a rotation rather than by a rotation-reflection (that is, so that the ordered basis , , , is also consistent with the same fixed choice of orientation as , , , ). Therefore, once one has selected an orientation (that is, a system of axes that is universally denoted as right-handed), one can determine the left or right character of a specific isoclinic rotation.