  The tree-level string effective action is known to contain quartic Riemann
terms with coefficient $\zeta(3)\alpha'^3$. In the case of the type II string
this is the first $\alpha'$ correction. We use the requirement that the action
reduced on a $d$-torus should have an $O(d,d)$ symmetry to find the B-field
couplings up to fifth order in fields. The answer turns out to have a
surprisingly intricate structure.
