  The irreducible bases of the group space of the icosahedral double groups
{\bf I'} and {\bf I$_{h}'$} are calculated explicitly. Applying those bases on
the spin states $|j,\mu>$, we present a simple formula to combine the spin
states into the symmetrical adapted bases, belonging to a given row of a given
irreducible representations of {\bf I'} and {\bf I$_{h}'$}.
