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We analyse the renormalization of the of two-nucleon interaction with multiple subtractions in peripheral waves considering two chiral forces at N3LO. Phase shifts at low energies are then computed with several subtraction points below μ=10 fm−1. We show that for most peripheral waves the phase shifts have nearly no dependence on the renormalization scale. In two cases the phase shifts converge slowly as the renormalization scale approaches μ=1 fm−1 and in one case the phase shifts presented oscillations with respect to the subtraction point μ.