  We present the variability study of broad absorption lines (BALs) in a
uniformly radio-selected sample of 28 BAL quasars using the archival data from
the FIRST Bright Quasar Survey (FBQS) and the Sloan Digital Sky Survey (SDSS),
as well as those obtained by ourselves, covering time scales $\sim 1-10$ years
in the quasar's rest-frame. To our surprise, 5 quasars showing strong
variations are all belong to a special subclass of overlapping iron low
ionization BAL (OFeLoBAL) quasars, however, other 4 non-overlapping FeLoBALs
(non-OFeLoBALs) are invariable except one case with weak optical depth change.
Meanwhile, we also find 6 typical variations of high-ionization and
low-ionization BALs in this BAL quasar sample. Photoionization models suggest
that OFeLoBALs are formed in a relative dense ($n_e>10^6$ cm$^{-3}$) outflows
at a distance from the subparsec to the dozens of parsecs from the continuum
source. They differ from those of non-OFeLoBALs, which are likely produced by
low-density gas, locating at a distance of hundreds to thousands parsecs. Thus,
OFeLoBALs and non-OFeLoBALs, i.e., FeLoBALs with/without strong BAL variations,
perhaps represent the bimodality of Fe II absorption, the former is located in
the active galactic nucleus environment rather than the host galaxy. We suggest
that high density and small distance are the necessary conditions that cause
OFeLoBALs. As suggested in the literature, strong BAL variability is possibly
due to variability of the covering factor of BAL regions caused by clouds
transiting across the line of sight rather than ionization variations.
