In terms of the irreducible bases of the group space of the octahedral double
group {\bf O'}, an analytic formula is obtained to combine the spin states
$|j,\mu \rangle$ into the symmetrical adapted bases, belonging to a given row
of a given irreducible representation of {\bf O'}. This method is effective for
all double point groups. However, for the subgroups of {\bf O'}, there is
another way to obtain those combinations. As an example, the correlations of
spin states for the tetrahedral double group {\bf T'} are calculated
explicitly.