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A perturbative unitary conjugation eliminating couplings between chosen separated energy sectors. For $H=H_0+V$ and an anti-Hermitian $S$ satisfying $[S,H_0]=-V$ at leading order, the transformed Hamiltonian contains $\frac{1}{2}[S,V]$ at second order. Exactly resonant coupled states must be retained in a common block. The method was used for the Anderson-to-Kondo relation by John Robert Schrieffer and P. A. Wolff.