A thrust reverser for an aircraft propulsion unit, comprising an evacuation structure comprising one or more openings, a movable structure and a fixed structure, the movable structure and the fixed structure delimiting a flow path capable of channeling an air flow in a longitudinal direction (D1) when the thrust reverser is in a direct jet position, the movable structure being movable between the direct jet position and a reverse jet position providing a radial evacuation of at least one portion of the air flow through the evacuation structure, wherein the thrust reverser comprises at least one closure membrane arranged to deflect at least one portion of the air flow in a direction of the evacuation structure when the thrust reverser is in the reverse jet position and an intermediate structure movable in rotation relative to the fixed structure about an axis coincident with the longitudinal direction (D1), a portion of the at least one closure membrane being fixed to the fixed structure, another portion of the at least one closure membrane being fixed to the intermediate structure.