The invention relates to a polymer matrix suitable for the transdermal administration of rotigotine [(−)-5, 6, 7, 8-tetrahydro-6-[propyl[2-(2-thienyl)ethyl]amino]-1-naphtol], containing a matrix for the transdermal administration of rotigotine [(−)-5, 6, 7, 8-tetrahydro-6-[propyl[2-(2-thienyl)ethyl]amino]-1 naphtol], containing a matrix polymer which is supersaturated with a rotigotine base. Said polymer matrix is characterised in that the part of the rotigotine which is not dissolved in the matrix polymer is dispersed in the matrix polymer as amorphous particles having a maximum mean diameter of 30 μm, and the matrix is free of solubilisers, crystallisation inhibitors and dispersants. The invention also relates to a flat device for the transdermal administration of rotigotine, containing the above-mentioned, preferably silicon-based polymer matrix which is supersaturated with rotigotine, and a rear layer which is impermeable to the active ingredient.