  We study in this paper a new family of stable algebraic symplectic vector bundles of rank $ 2n $ on the complex projective space $P^{2n+1}$ whose classical null correlation bundles belongs. We show that these bundles are invariant under a miniversal deformation. We also study the sufficient cohomological conditions for a symplectic vector bundle on a projective variety to be stable. 
Fibr\'e vectoriel de 0-corr\'elation pond\'er\'e sur l'espace $P^{2n+1}$