Recently, imposing the gauge-symmetry and the T-duality constraints on the string frame effective actions of type II superstring theories at order $\\\\alpha\\\'^3$, the NS-NS couplings have been found in a particular scheme which has 445 couplings in 15 different structures. In this paper, using a field redefinition, we write them in terms of 251 couplings which appear in 9 different structures. The 9 structures involve only Riemann curvature, $H_{\\\\alpha\\\\beta\\\\mu}$ and $\\\\nabla_{\\\\alpha}H_{\\\\beta\\\\mu\\\\nu}$. The number of couplings in the structures $R^4$, $H^8$, $H^6R$, $H^4R^2$, $H^2R^3$ are $2$, $2$, $1$, $7$, $22$, respectively, and the number of couplings in the structures $(\\\\nabla H)^4$, $(\\\\nabla H)^2R^2$, $(\\\\nabla H)^2 H^4$, $(\\\\nabla H)^2 H^2R$ are $12$, $22$, $77$, $106$, respectively. The new couplings are also fully consistent with the sphere-level S-matrix element of four NS-NS vertex operators.

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