A motor-vehicle suspension system of the MacPherson type comprising: - a pair of wheel supports; - two shock absorbers each having a body bolted to a corresponding wheel support with a top end connected to the structure of the motor vehicle; - a leaf spring, which counters the vertical movements of the two wheel supports, is set transverse to the longitudinal direction of the motor vehicle and has two ends connected to the respective wheel supports; - said leaf spring is made of a single piece having opposite ends each having a forked shape, with two prongs (7, 70) made of a single piece with said leaf spring, wherein each prong (7, 70) is connected separately to the corresponding wheel support by means of an elastic support or a ball joint (E1, E2); and - said suspension system does not comprise other connection elements between each wheel support and the structure of the motor vehicle so that said transverse leaf spring can be used also as auxiliary frame on which the components of the suspension can be assembled prior to installation on the structure of the motor vehicle. said suspension system being characterized in that: - said leaf spring is connected to the structure of the motor vehicle via four elastic supports; and - one of the two prongs (7, 70) of each end of the leaf spring is connected to the corresponding wheel support by means of an elastic support in the form of a bushing with axis parallel to the longitudinal direction of the motor vehicle, having an external cylindrical reinforcement inserted in a metal terminal connected to the leaf spring, and the other prong (7, 70) of each end of the leaf spring is connected to the corresponding wheel support by means of a ball joint having an external cylindrical reinforcement inserted in a seat of the leaf spring. - a pair of wheel supports; - two shock absorbers each having a body bolted to a corresponding wheel support with a top end connected to the structure of the motor vehicle; - a leaf spring, which counters the vertical movements of the two wheel supports, is set transverse to the longitudinal direction of the motor vehicle and has two ends connected to the respective wheel supports; - said leaf spring is made of a single piece having opposite ends each having a forked shape, with two prongs (7, 70) made of a single piece with said leaf spring, wherein each prong (7, 70) is connected separately to the corresponding wheel support by means of an elastic support or a ball joint (E1, E2); and - said suspension system does not comprise other connection elements between each wheel support and the structure of the motor vehicle so that said transverse leaf spring can be used also as auxiliary frame on which the components of the suspension can be assembled prior to installation on the structure of the motor vehicle. - said leaf spring is connected to the structure of the motor vehicle via four elastic supports; and - one of the two prongs (7, 70) of each end of the leaf spring is connected to the corresponding wheel support by means of an elastic support in the form of a bushing with axis parallel to the longitudinal direction of the motor vehicle, having an external cylindrical reinforcement inserted in a metal terminal connected to the leaf spring, and the other prong (7, 70) of each end of the leaf spring is connected to the corresponding wheel support by means of a ball joint having an external cylindrical reinforcement inserted in a seat of the leaf spring.