A brake system and method for operating same for a vehicle having a master brake cylinder, a brake medium reservoir, a first wheel brake cylinder, into which a first brake medium volume is displaceable from the master cylinder, a second wheel brake cylinder, into which a second brake medium volume is displaceable from the master cylinder, and a pump, which is hydraulically connected to the brake medium reservoir, the first wheel brake cylinder being hydraulically connected to the pump via a first non-return valve and the second wheel brake cylinder being hydraulically connected to the pump via a second non-return valve so that the pump can pump a third brake medium volume from the brake medium reservoir through the first non-return valve into the first wheel brake cylinder and a fourth brake medium volume from the brake medium reservoir through the second non-return valve into the second wheel brake cylinder.