  We find specific polarizations of components of a bichromatic field, which
allow one to prepare pure superposition states of atoms, using the coherent
population trapping effect. These $m$$-$$m$ states are prepared in the system
of Zeeman substates of the ground-state hyperfine levels with arbitrary angular
momenta $F_1$ and $F_2$. It is established that, in general case $m\ne 0$, the
use of waves with elliptical polarizations ($\epsilon_1$$\perp$$\epsilon_2$
field configuration for alkali metal atoms) is necessary for the pure state
preparation. We analytically show an unique advantage of the D1 line of alkali
metal atoms, which consists in the possibility to generate pure $m$$-$$m$
states even in the absence of spectral resolution of the excited-state
hyperfine levels, contrary to the D2 line.
