  In this paper we classify all non-Berwaldian Randers metrics of Douglas type
arising from invariant hyper-Hermitian metrics on simply connected
four-dimensional real Lie groups. Also, the formulas of the flag curvature are
given and it is shown that, in some directions, the flag curvature of the
Randers metrics and the sectional curvature of the hyper-Hermitian metrics have
the same sign.
