  Iron telluride FeTe is known to display bicollinear magnetic order at low
temperatures together with a monoclinic lattice distortion. Because the
bicollinear order can involve two different wavevectors $(\pi/2,\pi/2)$ and
$(\pi/2,-\pi/2)$, symmetry considerations allow for the possible stabilization
of a nematic state with short-range bicollinear order coupled to monoclinic
lattice distortions at a $T_S$ higher than the temperature $T_N$ where
long-range bicollinear order fully develops. As a concrete example, the
three-orbitals spin-fermion model for iron telluride is studied with an
additional coupling $\tilde\lambda_{12}$ between the monoclinic lattice strain
and an orbital-nematic order parameter with $B_{2g}$ symmetry. Monte Carlo
simulations show that with increasing $\tilde\lambda_{12}$ the first-order
transition characteristic of FeTe splits and bicollinear nematicity is
stabilized in a (narrow) temperature range. In this new regime the lattice is
monoclinically distorted and short-range spin and orbital order breaks
rotational invariance. A discussion of possible realizations of this exotic
state is provided.
