  We study the Post-Newtonian approach implemented to the Einstein-Hilbert
action adding the cosmological constant $\Lambda$ at 1PN order. We consider
very small values of $\Lambda$ to derive the Lagrangian of a two body compact
system at the center of mass frame at 1PN. Furthermore, the phase function
$\phi(t)$ is obtained from the balance equation and the two polarizations
$h_{+}$ and $h_{\times}$ are also calculated. We observe changes due to
$\Lambda$ only at very low frequencies and we notice that it plays the role of
"stretch" the spacetime such that both amplitudes become smaller; however,
given its nearly negligible value, $\Lambda$ has no relevance at higher
frequencies whatsoever.
