  We have found the precise stability region of the half quantum vortex (HQV)
for superfluid $^3$He A phase confined in parallel plates with a narrow gap
under rotation. Standard Ginzburg-Landau free energy, which is well
established, is solved to locate the stability region spanned by temperature
$T$ and rotation speed ($/Omega$). This $/Omega$-$T$ stability region is wide
enough to check it experimentally in available experimental setup. The detailed
order parameter structure of HQV characterized by A$_1$ core is given to
facilitate the physical reasons of its stability over other vortices or
textures.
