A formaldehyde-free sizing composition for products based on fibers, in particular mineral fibers, such as fibers of glass or of rock, includes at least one non-reducing sugar, and at least one inorganic acid ammonium salt, preferably chosen from ammonium sulfates, phosphates, nitrates and carbonates. Another subject matter of the present invention is the products thus obtained, in particular thermal and/or acoustic insulators based on mineral wool and veils of nonwoven mineral fibers, and their process of manufacture.