  We study the nucleon-nucleon interaction up to next-to-next-to-leading order
using time-ordered perturbation theory in the framework of manifestly
Lorentz-invariant chiral effective field theory. We present the two-pion
exchange contribution at one-loop level, which is consistent with the
corresponding non-relativistic expressions in the large-nucleon-mass limit.
Using the Born series truncated at one-loop order, we calculate the phase
shifts and mixing angles of the partial waves with the angular momentum $l\geq
2$. Comparing with the results of non-relativistic formulation, we find an
improved description of the phase shifts for some $D$ waves such as the $^3D_3$
one. For the other partial waves, both approaches show the globally similar
results.
