  In this paper we obtain a decoupling feature of the random interlacements
process $\mathcal{I}^u \subset \mathbb{Z}^d$, at level $u$, $d\geq 3$. More
precisely, we show that the trace of the random interlacements process on two
disjoint finite sets, $\textsf{F}$ and its translated $\textsf{F}+x$, can be
coupled with high probability of success, when $\|x\|$ is large, with the trace
of a process of independent excursions, which we call the noodle soup process.
As a consequence, we obtain an upper bound on the covariance between two
$[0,1]$-valued functions depending on the configuration of the random
interlacements on $\textsf{F}$ and $\textsf{F}+x$, respectively. This improves
a previous bound obtained by Sznitman in [12].
