  This work gives an explicit exact expression for the Thomas precession
arising in the framework of Special Theory of Relativity as the spatial
rotation resulting from two subsequence Lorentz boosts. The final result for
the orthogonal matrix of Thomas precession is given by Eqs. (21)--(25). A
trivial calculation leads to the compact formula (26) for the angle of rotation
due to Thomas precession.
  In the framework of Gaia the special-relativistic Thomas precession is an
important step in the derivation of an aberrational formula with the
Mansouri-Sexl parameters. The latter formula will be used to test the Local
Lorentz Invariance with Gaia data as will be explained elsewhere.
