  In our previous papers we described the structure of trajectories of the
symmetric Toda system on normal real forms of various Lie algebras and showed
that it was totally determined by the Hasse diagram of the Bruhat order on the
corresponding Weil group. This note deals with the simplest non-split real Lie
algebra, $\mathfrak{so}(2,4)$. It turns out, that the phase diagram in this
case is also closely related with the Bruhat order of the relative Weyl group,
but a bit more information is necessary to describe the dimensions of the
trajectory spaces.
