  In this article we review the recent results about the flag curvature of
invariant Randers metrics on homogeneous manifolds and by using a counter
example we show that the formula which obtained for the flag curvature of these
metrics is incorrect. Then we give an explicit formula for the flag curvature
of invariant Randers metrics on the naturally reductive homogeneous manifolds
$(G/H,g)$, where the Randers metric induced by the invariant Riemannian metric
$g$ and an invariant vector field $\tilde{X}$ which is parallel with $g$.
