  Experimentally it is still challenging to epitaxially grow Bi(111) bilayer
(BL) on conventional semiconductor substrate. Here, we propose a substrate of
$\beta-$In$_2$Se$_3$(0001) with van der Waals like cleavage and large band gap
of 1.2~eV. We have investigated the electronic structure of BL on one
quintuple-layer (QL) $\beta-$In$_2$Se$_3$(0001) using density functional theory
calculation. It is found that the intermediate hybridization between BL and one
QL $\beta-$In$_2$Se$_3$(0001) results in the formation of bands with giant
Rashba spin splitting in the large band gap of the substrate. Furthermore the
Rashba parameter $\alpha_R$ can be increased significantly by tensile strain of
substrate. Our findings provide a good candidate substrate for BL growth to
experimentally realize spin splitting Rashba states with insignificant effect
of spin degenerate states from the substrate.
