Abstract: In a process for cleaning a glass window of a motor vehicle with a wiper apparatus having a wiper, including applying a washer fluid including a cleaning agent and water to the glass window from a container located in the motor vehicle, and moving the wiper over the glass window with the wiper apparatus to at least partially clean the glass window with the washer fluid, the improvement includes spraying or blowing a polishing composition containing a metal oxide powder on the glass window, advantageously from a container located in the motor vehicle, and cleaning the glass window with the polishing composition containing the metal oxide powder by action of the wiper together with the polishing composition, so that, when present on the glass window, a hydrophobic dirt layer formed on the glass window is removed. The metal oxide powder advantageously has a particle size from 10 nm to 1 micrometer and is cerium oxide.