We define a generalization of the first-order cut-elimination method CERES to higher-order logic. At the core of lies the computation of an set of sequents from a proof π of a sequent S. A refutation of in a higher-order resolution calculus can be used to transform cut-free parts of π into a cut-free proof of S. An example illustrates the method and shows that can produce meaningful cut-free proofs in mathematics that traditional cut-elimination methods cannot reach.