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We generalize the results in [2] giving a reduction algorithm allowing tocompute the index of seaweed subalgebras of classical simple Lie algebras. Wethus are able to obtain the index of some interesting families of seaweedsubalgebras and to give new examples of large classes of Frobenius Lie algebrasamong them.

Indice des sous-alg\`ebres biparaboliques d'une alg\`ebre de Lie simple classique