  We present a homogeneous set of accurate atmospheric parameters for a sample
of eleven very metal-poor (-3.32 <= [Fe/H] <= -2.61) stars in the Sextans dwarf
spheroidal galaxy (dSph) and the non-local thermodynamic equilibrium (NLTE)
abundances of, at least, seven chemical elements based on high-resolution
UVES/VLT and HDS/Subaru spectra. For each star, its effective temperature and
surface gravity were derived from the spectral energy distribution and the
known distance, and the Fe abundance was obtained as the average from lines of
Fe I and Fe II. Based on abundances of Mg, Ca, and Ti, we show that all the
investigated stars reveal alpha-enhancements of 0.4~dex to 0.2~dex, and there
is a hint of a decline in alpha/Fe for [Fe/H] > -2.8. The Sextans stars are
deficient in Ba. The new result is an extremely tight relation between Ba and
Mg, suggesting their common origin in massive stars and Ba synthesis in the
r-process events on the timescales of standard supernovae. The exception is a
C-enhanced star S 15-19 which is strongly enhanced in Ba. This star is unlikely
to be a CEMP-s star because of low abundances of Sr and Y ([Y/Fe] < -1) that
are produced in the s-process as efficiently as Ba and a non-detection of
variation in the radial velocity. No distinctions from the Milky Way halo and
the Sculptor and Ursa Minor dSphs were found in a history of early enrichment
in Na and Ni, namely, the Sextans stars are deficient in Na and have
close-to-solar Ni/Fe.
