Invertible disformal transformations with higher derivatives

We consider a higher-derivative generalization of disformal transformations in $D$-dimensional spacetime and clarify the conditions under which they form group with respect to matrix product functional composition. These allow us systematically construct inverse transformation fully covariant manner. Applying invertible generalized known ghost-free scalar-tensor theories, we obtain novel class whose action contains third- or higher-order derivatives scalar field as well nontrivial derivative couplings curvature tensor.