DeDion Axle

De Dion suspension is almost as old as the car itself. Designed by Count De Dion, the axle was mounted to a vertical track and slides up and down it.  

It has been used by the likes of Maserati 250F with a transverse leaf spring to great success.  The old Rover  3.5/2000/2200 , Caterhams super Seven and can still be found Today  on the Aston Martin Vantage.  It has even had outings in F1 right up to the 70's

Although independent suspensions were invented decades ago, non-independent suspensions still dominated the market until the late 70s. The first reason was: cheap. The second reason: it offers quite good handling despite of poor ride. Since the wheels are rigidly linked by an axle, they remain perpendicular to the road surface regardless of body roll. Therefore the car corners quite stable. In contrast, in many types of independent suspensions, camber angle may be changed due to body roll.

However, a live axle has too much unsprung weight, and leads to poor ride quality. Therefore many budget sports cars or coupes chose DeDion Axle (rear) suspensions over live axle.

DeDion axle suspension has much less unsprung weight because the final drive / differential and driving shafts are not rigidly attached to the wheels. Like independent suspensions, they are part of the car body and flexibly linked to the wheels by universal joints. In other words, they are sprung.

The wheels are interconnected by a DeDion Tube, which has a sliding joint to permit wheel track variation during suspension movement, this helps in  refining ride quality too. The DeDion tube keeps both wheels parallel to each other under all conditions, so they are always perpendicular to the road surface regardless of body roll.
 

Just to help some more The brakes can also be mounted inboard  and therefore reduce the unsprung weight from the wheels some more.