  In a supersymmetric compactification of Type II supergravity, preservation of
${\cal{N}} = 1$ supersymmetry in four dimensions requires that the structure
group of the generalized tangent bundle $TM \oplus T^*M$ of the six dimensional
internal manifold $M$ is reduced from $SO(6,6)$ to $SU(3) \times SU(3)$. This
topological condition on the internal manifold implies existence of two
globally defined compatibe pure spinors $\Phi_1$ and $\Phi_2$ of non-vanishing
norm. Furthermore, these pure spinors should satisfy certain first order
differential equations. In this paper, we show that Non-Abelian T-duality
(NATD) is a solution generating transformation for these pure spinor equations.
We first show that the pure spinor equations are covariant under $Pin(d,d)$
transformations. Then, we use the fact NATD is generated by a coordinate
dependent $Pin(d,d)$ transformation. The key point is that the flux produced by
this transformation is the same as the geometric flux associated with the
isometry group, with respect to which one implements NATD. We demonstrate our
method by studying NATD of certain solutions of Type IIB supergravity with
$SU(2)$ isometry and $SU(3)$ structure.
