  A renormalization scheme for the nucleon-nucleon (NN) interaction based on a
subtracted T-matrix equation is proposed and applied to the one-pion-exchange
potential supplemented by contact interactions. The singlet and triplet
scattering lengths are given to fix the renormalized strengths of the contact
interactions. With only one scaling parameter ($\mu$), the results show an
overall very good agreement with neutron-proton data, particularly for the
observables related to the triplet channel. The agreement is qualitative in the
$^1S_0$ channel. Between the low-energy NN observables we have examined, the
mixing parameter of the $^3S_1-^3D_1$ states is the most sensible to the scale.
The scheme is renormalization group invariant for $\mu\to\infty$.
