  A general rule is presented for the decomposition of the direct product of
irreducible representation at arbitrary Brillouin zone point $\bf{R}$ with its
negative: the number of the appearences of the zone center representation
equals the dimensionality of the representation. This rule is applicable for
all space groups. Although in most situations the interesting physics takes
place at high symmetry points in the Brillouin zone, this general rule is
useful for situations where double excitations are considered. It is shown that
double excitations from arbitrary Brillouin point $\bf{R}$ have the right
symmetry to participate in all optical experiments regardless of polarization
directions.
