  We obtain a first order post-Minkowskian two-body effective potential whose
post-Newtonian expansion directly reproduces the Einstein-Infeld-Hoffmann
potential. Post-Minkowskian potentials can be extracted from on-shell
scattering amplitudes in a quantum field theory of scalar matter coupled to
gravity. Previously, such potentials did not reproduce the
Einstein-Infeld-Hoffmann potential without employing a suitable canonical
transformation. In this work, we resolve this issue by obtaining a new
expression for the first-order post-Minkowskian potential. This is accomplished
by exploiting the reference frame dependence that arises in the scattering
amplitude computation. Finally, as a check on our result, we demonstrate that
our new potential gives the correct scattering angle.
