  It is known that the anomalous D$_p$-brane Chern-Simons couplings are not
consistent with the standard rules of T-duality. Using compatibility of these
couplings with the linear T-duality transformations, the B-field gauge
transformations and with the general coordinate transformations as guiding
principles we find new couplings at order $O(\alpha'^2)$ for ${\cal
C}^{(p-3)}$, ${\cal C}^{(p-1)}$, ${\cal C}^{(p+1)}$ and ${\cal C}^{(p+3)}$.
