  The tree-level string effective action reduced from $D$ to $D-d$ dimensions
possesses a continuous $O(d,d)$ symmetry, closely related to T-duality. A
necessary condition for a higher derivative correction to preserve this
symmetry is that certain $O(d,d)$ violating terms which appear in the
dimensional reduction have to cancel out. We use this idea to complete the
quartic Riemann correction with all terms involving five NS-NS sector fields.
The resulting Lagrangian is considerably simpler than expressions that have
previously appeared in the literature.
