A new dynamical propensity rule for transitions of a system crossing the barrier from one potential minimum to one another is derived from dynamical system theory. The rule is based on the existence of a no-return dividing hypersurface in the system's phase space in the vicinity of saddles of the multidimensional potential surface of a strongly coupled, chaotic system. We present numerical evidence of the rule's validity by applying it to the rearrangements of a cluster of six argon atoms.