  Recently, for principal chiral models and symmetric coset sigma models, Hoare
and Tseytlin proposed an interesting conjecture that the Yang-Baxter
deformations with the homogeneous classical Yang-Baxter equation are equivalent
to non-abelian T-dualities with topological terms. It is significant to examine
this conjecture for non-symmetric (i.e., non-integrable) cases. Such an example
is the $W_{2,4}\times T^{1,1}$ background. In this note, we study Yang-Baxter
deformations of type IIB string theory defined on $W_{2,4}\times T^{1,1}$ and
the associated T-dual models, and show that this conjecture is valid even for
this case. Our result indicates that the conjecture would be valid beyond
integrability.
