A shedding assembly with a shedding machine includes an eccentric system which defines an eccentric center distance, a first connecting rod, actuated by the eccentric system to actuate a first lever and defining a connecting rod center distance, and a second connecting rod, making the first lever pivot in conjunction with that of a second lever to actuate a heald frame. To facilitate adjustment, the shedding machine includes an adjustment system, which allows at least one adjustment configuration where one of the center-to-center distances is adjustable, as well as a follower member equipping the second connecting rod. The shedding assembly comprises a flap for moving the second connecting rod by driving the follower member for adjusting the center distance when the adjustment system is in the adjustment configuration.