We begin by considering the standard Courant bracket, obtained from the Poisson bracket algebra of the symmetry generators governing general coordinate transformations and local gauge transformations in the case of a closed bosonic string. It is well known that this bracket can be twisted by various transformations, resulting in different string fluxes. We introduce a transformation that simultaneously twists by a 2-form $B$ and a bi-vector $\theta$. When these objects are interpreted as string fields, namely the Kalb-Ramond field and the non-commutativity parameter, the transformation is manifestly self-T-dual. The resulting twisted Courant bracket contains all fluxes.