Cleaning device comprising a support (1) with at least one cleaning surface (2) on which raised cleaning islands (3) are arranged at certain distances (4, A, B, C, D, E, 9) from each other such that the cleaning islands (3) are surrounded on all sides by storage spaces (5) for holding dirt. The size of the storage spaces (5) decreases steadily from at least one edge (6) of the cleaning surface at least to the middle of the cleaning surface (2) in the cleaning direction (7).