A convertible motor vehicle (100) has a passenger compartment accommodating a driver seat and a passenger seat (105) and a trunk (103), where fastening members (110) are provided to support baggage retaining catches; a transport structure (101) for a patient is fittable within the motor vehicle (100) and is provided with a pair of rails (1, 2) for a stretcher (30); the rails (1, 2) are supported by front and rear supporting members (4, 17) and have a front portion which is arranged above a reclined backrest of the passenger side front seat (105) when the transport structure (101) is fitted; furthermore, again when the transport structure (101) is fitted, the rear supporting members (17) are releasably fastened to the fastening members (110).