  Removing the field redefinitions, the Bianchi identities and the total
derivative freedoms from the general form of gauge invariant NS-NS couplings at
order $\alpha'^3$, we have found that the minimum number of independent
couplings is 872. We find that there are schemes in which there is no term with
structures $R,\,R_{\mu\nu},\,\nabla_\mu H^{\mu\alpha\beta}$, $
\nabla_\mu\nabla^\mu\Phi$. In these schemes, there are sub-schemes in which,
except one term, the couplings can have no term with more than two derivatives.
In the sub-scheme that we have chosen, the 872 couplings appear in 55 different
structures. We fix some of the parameters in type II supersting theory by its
corresponding four-point functions. The coupling which has term with more than
two derivatives is constraint to be zero by the four-point functions.
