  We report on observation of an unconventional structure of the quantum Hall
effect (QHE) in a $ p$-type HgTe/Cd$_x$Hg$_{1-x}$Te double quantum well (DQW)
consisting of two HgTe layers of critical width. The observed QHE is a
reentrant function of magnetic field between two $i=2$ states (plateaus at
$\rho_{xy}=h/ie^2$) separated by an intermediate $i=1$ state, which looks like
some anomalous peak on the extra-long $i=2$ plateau when weakly expressed. The
anomalous peak apparently separates two different regimes: a traditional QHE at
relatively weak fields for a small density of mobile holes $p_s$ and a
high-field QH structure with a $2-1$ plateau--plateau transition corresponding
to much larger $p_s$. We show that only a part of holes, residing in an
additional light hole subband in the DQW, participate in QHE at weak fields
while the rest of holes is excluded into the reservoir formed in the lateral
maximum of the valence subband. All the holes come into play at high fields due
to a peculiar behavior of the zero-mode levels.
