A deformable film has a decorative surface featuring a completely matt appearance. For this purpose, the deformable film has a decorative surface provided with at least one coating comprising the following constituents: (a) an aqueous dispersion of a hydroxy-functional prepolymer, obtainable by conversion of at least one of the following components: (i) a component having hydroxyl groups, (ii) a polyester polyol having hydroxyl groups, (iii) a polyisocyanate having isocyanate groups, (iv) a compound having at least two groups reactive toward isocyanate groups and at least one group capable of anion formation, (v) water, where components (i) to (iii) and the ratio of components (i) to (iii) are selected such that an excess of hydroxyl groups is present relative to the isocyanate groups, and (b) nanoparticles having a number-average particle size of 1 to 1000 nm and (c) a crosslinker having at least two groups reactive toward hydroxyl groups.