An aircraft nacelle includes an air intake followed at the upper part by a part that is integral with the mast, called a cap, and at least one door with a curved profile that includes a stiffening device arranged at the edge upstream from the door and which includes: a flexible element that follows the curved profile of the door between two remote anchoring points, at least one safety index including a latch pivotable around an axis of rotation, and connected to the door so as to occupy a locked position in which the end of the latch rests against the inside surface of an edge upstream from the door, and an unlocked position in which the end of the latch is offset relative to the edge, whereby in the locked position, the latch prevents the scooping phenomena by limiting movements of the door in the radial direction toward the outside of the nacelle, and elements for stretching the flexible element between the two anchoring points and for controlling the pivoting in the locked position of the latch.