A method for making a composite structure or a portion of a composite structure of a braking band of a brake disc, unusually capable of obtaining a structure with an especially long life, comprising at least the following steps: making a composite ceramic structure, comprising carbon fibre filaments, silicon and silicon carbides, obtaining a body of a braking band comprising at least one braking surface; processing said braking surface removing a surface layer so as to have carbon not bonded with the silicon on surface; removing at least partly the carbon not bonded with silicon from the surface; depositing an anchoring substrate on said braking surface; and depositing a protective coating on said anchoring substrate.