  A methodology to renormalize the nucleon-nucleon interaction, using a
recursive multiple subtraction approach to construct the kernel of the
scattering equation, is presented. We solve the subtracted scattering equation
with the next-leading-order (NLO) and next-to-next-leading-order (NNLO)
interactions. The results are presented for all partial waves up to $j=2$,
fitted to low-energy experimental data. In our renormalizaton group invariant
method, when introducing the NLO and NNLO interactions, the subtraction energy
emerges as a renormalization scale and the momentum associated with it comes to
be about the QCD scale ($\Lambda_{QCD}$), irrespectively to the partial wave.
