  We study Manin triples for a reductive Lie algebra, $\g$. First, we
generalize results of E. Karolinsky, on the classification of Lagrangian
subalgebras (cf. KAROLINSKY E., {\em A Classification of Poisson homogeneous
spaces of a compact Poisson Lie group}, Dokl. Ak. Nauk, 359 (1998), 13-15).
Then we show that, if $\g$ is non commutative, one can attach, to each Manin
triple in $\g$, an other one for a strictly smaller reductive complex Lie
subalgebra of $\g$. We study also the inverse process.
