A metallic sealing assembly between a rotating shaft and a fixed frame comprises: a flexible metallic seal having two tori, inner and outer, that are concentric and of different average diameters, comprising a metal envelope which encases and holds the inner and outer tori; a shaft rotating about an axis of rotation, comprising an annular shoulder against which the seal comes to press; a counter-face, comprising a contact face against which the seal comes to press; a wedge block positioned around the rotating shaft such that the seal is held between the wedge block and the contact face, the wedge block mounted to slide on the rotating shaft; a metal part which forms a cap through which the rotating shaft passes and which is secured to the frame and/or to the counter-face, the rotating shaft being free to rotate with respect to the cap and axially secured to the cap.