  Let $M$ be a simply connected closed manifold of dimension $n$. We study the
rational homotopy type of the configuration space of 2 points in $M$, $F(M,2)$.
When $M$ is even dimensional, we prove that the rational homotopy type of
$F(M,2)$ depends only on the rational homotopy type of $M$. When the dimension
of $M$ is odd, for every $x\in H^{n-2} (M, \mathbb{Q})$, we construct a
commutative differential graded algebra $C(x)$. We prove that for some $x \in
H^{n-2} (M; \mathbb{Q})$, $C(x)$ encodes completely the rational homotopy type
of $F(M,2)$. For some class of manifolds, we show that we can take $x=0$.
