  In several Fe-based superconductors, slight $C_4$ symmetry breaking occurs at
$T^*$, which is tens of Kelvin higher than the structural transition
temperature $T_S$. In this "hidden" nematic state at $T_S<T<T^*$, the
orthorhombicity is tiny [$\phi=(a-b)/(a+b) \ll 0.1$%], but clear evidences of
bulk phase transition have been accumulated. To explain this long-standing
mystery, we propose the emergence of antiferro-bond (AFB) order with the
antiferro wavevector ${\bf q}=(0,\pi)$ at $T=T^*$, by which the characteristic
phenomena below $T^*$ are satisfactorily explained. This AFB order originates
from the inter-orbital nesting between the $d_{xy}$-orbital hole-pocket and the
electron-pocket, and this inter-orbital bond order naturally explains the
pseudogap, band-folding, and tiny nematicity that is linear in $T^*-T$. The
hidden AFB order explains key experiments in both BaFe$_2$As$_2$ and NaFeAs,
but it is not expected to occur in FeSe because of the absence of the
$d_{xy}$-orbital hole-pocket.
