  Within density functional theory, we study bulk band structure and surface
states of BiTeBr. We consider both ordered and disordered phases which differ
in atomic order in the Te-Br sublattice. On the basis of relativistic ab-initio
calculations, we show that the ordered BiTeBr is energetically preferable as
compared with the disordered one. We demonstrate that both Te- and
Br-terminated surfaces of the ordered BiTeBr hold surface states with a giant
spin-orbit splitting. The Te-terminated surface-state spin splitting has the
Rashba-type behavior with the coupling parameter \alpha_R ~ 2 eV\AA.
