  We reconsider the issue of Berezinskii-Kosterlitz-Thouless (BKT) transition
into an insulating state in the Coulomb-dominated Josephson junction arrays. We
show that previously predicted picture of the Cooper-pair BKT transtion at T =
T_2 is valid only under the condition that T_2 is considerably below the
parity-effect temperature (which is usually almost 10 times below the value of
superconductive transition temperature), and even in this case it is not a
rigorous phase transition but only a crossover, whereas the real phase
transition takes place at T_1 = T_2/4. Our theory is in agreement with
available experimental data on Coulomb-dominated Josephson arrays and also
sheds some light on the origin of unusual reentrant temperature dependence of
resistivity in the array with nearly-criticial ratio of Coulomb to Josephson
energies.
