A self-climbing formwork has a stationary climbing shoe (18) structured for attachment to a wall anchor point and a climbing cylinder (10) having a lower end directly contacting the climbing shoe (18) to form a hinge, the hinge defining a pivoting movement of the climbing cylinder (10) relative to the climbing shoe (18). A support (30) is provided on an upper end of the climbing cylinder (10), the support (30) having a protrusion defining a U-shaped recess. A climbing rail (22) is structured to be held in position by the climbing shoe (18) relative to the anchor point and guided along the wall through cooperation with the climbing shoe (18). Upon extension of the climbing cylinder (10), the support (30) engages beneath an upper engagement point (24″, 24″) of the climbing rail (22) at the U-shaped recess to urge the climbing rail (22) in an upward direction.