  The Mazur principle give simple conditions for an irreducible unramified
$\overline{\mathbb{F}_l}$-representation coming from a modular form of level
$\Gamma_0(Np)$ to come for some modular form of level $\Gamma_0(N)$. The aim of
this work is to give a generalization of this principle in higher dimension for
some particular extended inner forms non quasi split of a unitary group
studying the torsion cohomology classes of Shimura varieties of
Kottwitz-Harris-Taylor type within its link with the local monodromy
degeneracy.
