  We use inelastic neutron scattering to show that long-range spin waves
arising from the static bicollinear antiferromagnetic (AF) order in FeTe, which
have twofold rotational symmetry in a fully detwinned crystal, rapidly dissolve
above $E\approx 26$ meV into ridges of scattering with fourfold rotational
symmetry and a nearly isotropic magnetic fluctuation spectrum. With increasing
temperature above $T_N\approx 68$ K, the twofold spin waves change into broad
regions of scattering with fourfold symmetry. Since the scattering patterns
from plaquette magnetic order generated within a bilinear biquadratic
Hamiltonian have fourfold rotational symmetry consistent with the high-energy,
spin-isotropic spin waves of FeTe, we conclude that the bicollinear AF state in
FeTe is quasidegenerate with plaquette magnetic order, providing evidence for
the strongly frustrated nature of the local moments in iron chalcogenide family
of iron-based superconductors.
