  In the present paper we study Randers metics of Berwald type on simply
connected 4-dimensional real Lie groups admitting invariant hypercomplex
structure. On these spaces, the Randers metrics arising from invariant
hyper-Hermitian metrics are considered. Then we give explicit formulas for
computing flag curvature of these metrics. By this study we construct two
4-dimensional Berwald spaces, one of them has non-negative flag curvature and
the other one has non-positive flag curvature.
