  We demonstrate that a four-boson limit-cycle independent of the Efimov one
appears in Hamiltonian systems at the unitary limit. The model interaction
contains two-, three- and four-body short-range potentials, which disentangle
the interwoven three- and four-boson cycles, for the universal trimer and
tetramer energy levels, respectively. The limit-cycle associated with the
correlation between the energies of two successive universal tetramer levels
for fixed weakly bound trimer is found to be largely model independent. This is
a universal manifestation of an independent four-boson scale associated with a
cycle beyond the Efimov one.
