It is not uncommon for rings to have Gabriel localizations which do not possess the unique rank (UR) property although the rings themselves do have UR. We show that if F is a Gabriel filter of right ideals on a ring R and RFis the corresponding Gabriel localization, then free RF−modules of ranks m and n are isomorphic if and only if some F-dense submodule of (R/Tf(R))mis isomorphic to some F-dense submodule of (R/TF(R))n, where TF(R) is the F-torsion ideal of R.