  Non-Abelian T-duality (NATD) is a solution generating transformation for
supergravity backgrounds with non-Abelian isometries. We show that NATD can be
described as a coordinate dependent O(d,d) transformation, where the dependence
on the coordinates is determined by the structure constants of the Lie algebra
associated with the isometry group. Besides making calculations significantly
easier, this approach gives a natural embedding of NATD in Double Field Theory
(DFT), a framework which provides an O(d,d) covariant formulation for effective
string actions. As a result of this embedding, it becomes easy to prove that
the NATD transformed backgrounds solve supergravity equations, when the
isometry algebra is unimodular. If the isometry algebra is non-unimodular, the
generalized dilaton field is forced to have a linear dependence on the dual
coordinates, which implies that the resulting background solves generalized
supergravity equations.
