Top of a convertible vehicle having an unfoldable headliner

A top of a convertible vehicle, comprising:

• a top linkage which can be displaced between a closed position, in which the top covers a vehicle interior, and a storage position, in which the vehicle interior is open toward the sky, and which has a link-age arrangement on either side of a vertical longitudinal center plane of the top, the linkage arrangement being covered by a headliner when in the closed position,
• wherein a fabric deflecting element for the headliner is attached to each of the linkage arrangements, the fabric deflecting element moving relative to a roof side rail when the top linkage is being displaced between the closed position and the storage position, an edge of the headliner being attached to the roof side rail,
• wherein the headliner slides on a fabric contact surface of the fabric deflecting element when the top linkage is being displaced between the storage position and the closed position;
• and
• wherein each fabric deflecting element is attached to the respective linkage arrangement via an articulation.