The following remarks are made on the applicability of the double dispersion approach to the Beth-Salpeter equation introduced previously. 1) Any invariant solution of the Bethe-Salpeter equation in ladder approximation satisfies the double dispersion representation when the total energy-momentum is space-lake. 2) There are some exceptional invariant solutions which are not given by the previous method in the equal-mass case, but the existence of such solutions is very unlikely in the unequal-mass case. 3) In the case of the general separated kernel the previous results give the correct solutions even if the kernel does not reproduce the double dispersion representation.