  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.
