Sur l'indice des sous-alg\`ebres biparaboliques de $\mathfrak{g}\mathfrak{l}(n)$

We give some properties on the index of seaweed subalgebras of the complex Lie algebra $\mathfrak{g}\mathfrak{l}(n)$ which allow to obtain formulas for the index of some interesting classes of this family and to give new families of Frobenius Lie algebras.