An anti-lightning system for a composite structure having an external surface liable to be subjected to an air flow, the aforementioned system including at least one electrically conducting strip and fasteners fastening the aforementioned strip to the structure, the aforementioned strip being electrically connected to an electrical earth for removing current. According the disclosed embodiments, the aforementioned strip has a shape intended to collaborate with a housing created at the aforementioned external surface so that the external surface of the strip lies flush with the aforementioned external surface of the structure, and the aforementioned fasteners include an upper part flush with the external surface of the strip.