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