  The lifting of $d_{xz}$-$d_{yz}$ orbital degeneracy is often considered a
hallmark of the nematic phase of Fe-based superconductors, including FeSe, but
its origin is not yet understood. Here we report a high resolution
Angle-Resolved Photoemission Spectroscopy study of single crystals of FeSe,
accounting for the photon-energy dependence and making a detailed analysis of
the temperature dependence. We find that the hole pocket undergoes a
fourfold-symmetry-breaking distortion in the nematic phase below 90~K, but in
contrast the changes to the electron pockets do not require fourfold
symmetry-breaking. Instead, there is an additional separation of the existing
$d_{xy}$ and $d_{xz/yz}$ bands - which themselves are not split within
resolution. These observations lead us to propose a new scenario of
"unidirectional nematic bond ordering" to describe the low-temperature
electronic structure of FeSe, supported by a good agreement with 10-orbital
tight binding model calculations.
