  We demonstrate the existence of a spin-nematic, moment-free phase in a
quantum four-spin ring exchange model on the square lattice. This unusual
quantum state is created by the interplay of frustration and quantum
fluctuations which lead to a partial restoration of SU(2) symmetry when going
from a four-sublattice orthogonal biaxial Neel order to this exotic uniaxial
magnet. A further increase of frustration drives a transition to a fully gapped
SU(2) symmetric valence bond crystal.
