In the system or method for sprinklering a building, the building has a water delivery pipe for delivery of water to at least two different floors of the building. On at least two floors, a respective sprinkler pipe with a plurality of sprinklers is installed. Also a respective pump is installed whose outlet is connected to the respective sprinkler pipe, and whose inlet is connected to the water delivery pipe. A respective sensor for the respective pump automatically activates the pump when at least one of the sprinklers is activated.