A braking system for a vehicle having two pairs of wheels, has two master cylinders operating as pumps, wherein each master cylinder is operated by its own brake pedal and controls the braking on one rear wheel, as well as on the front wheels through a valve for the disconnection of the front vehicle braking. Each master cylinder is of the tandem type including two sections, the first section controlling the braking of the front wheels through the valve, whereas the second section controls the braking of that rear wheel, being a part of the pair of rear wheels, which is associated with the master cylinder. The first sections of both master cylinders are supplied by a first oil reservoir and the second sections of both master cylinders are supplied by a second oil reservoir at least partially independent from the first oil reservoir.