  We examine the proposal that the dimensional reduction of the effective
action of perturbative string theory on a circle, should be invariant under
T-duality transformations. The T-duality transformations are the standard
Buscher rules plus some higher covariant derivatives. By explicit calculations
at order $\alpha'$ for metric, dilaton and B-field, we show that the T-duality
constraint can fix both the effective action and the higher derivative
corrections to the Buscher rules up to an overall factor. The corrections
depend on the scheme that one uses for the effective action. We have found the
effective action and its corresponding T-duality transformations in an
arbitrary scheme.
