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We give again a proof of non-homogeneous T1 theorem. Our proof consists ofthree main parts: a construction of a random dyadic lattice; an estimate ofmatrix coefficients of a Calder\'on--Zygmund operator with respect to randomHaar basis if a smaller Haar support is good; a clever averaging trick fromHyt\"onen's papers which uses the averaging over dyadic lattices to decomposeoperator into dyadic shifts eliminating the error term that was present in theprevious proofs by Nazarov--Treil--Volberg.

The proof of non-homogeneous T1 theorem via averaging of dyadic shifts