The invention relates to a substrate (10), especially a transparent glass substrate, equipped with a thin-film multilayer comprising, in alternation, “n” metallic functional films (40, 80, 120), in particular functional films based on silver or a metal alloy containing silver, and “(n+1)” antireflection coatings (20, 60, 100, 140), where n is an integer≧3, each antireflection coating comprising at least one antireflection film, so that each functional film (40, 80, 120) is located between two antireflection coatings (20, 60, 100, 140), characterized in that said multilayer comprises at least two high-refractive-index antireflection films (25, 145), each having a refractive index≧2.15 such that the antireflection coating (20) located under the first, starting from the substrate, functional film (40) and the antireflection coating located on the last, starting from the substrate, functional film each comprise at least one high-refractive-index antireflection film (25, 145) and each antireflection coating (60, 100) located between two functional films does not comprise a high-refractive-index film.