A sunshade assembly includes a flexible sunscreen and two opposed longitudinal guides for guiding longitudinal edges of the sunscreen. A rotatable winding shaft winds and unwinds the sunscreen. An operating beam is connected to the opposite transversal edge of the sunscreen. Two drive cables are connected to opposite ends of the operating beam. Two positioning members move with the operating beam. Each positioning member extends into a corresponding one of the opposed longitudinal guides. Each of the opposed longitudinal edges of the sunscreen near the opposite transversal edge is provided with a wing folded inward in a direction away from the respective positioning member, so that the wing and the respective positioning member are on opposite sides of the sunscreen. The wing accessible to the respective positioning member from the opposite side of the flexible sunscreen in order to engage the respective positioning member.