An assembly for a turbomachine nozzle having a longitudinal axis (X) includes an exhaust cone with an annular outer wall for guiding a primary air flow and an annular chamber placed radially inside said annular outer wall. The annular chamber includes an annular inner wall placed radially inside the annular outer wall of the exhaust cone. An exhaust case is placed upstream of the ejection cone. A connecting member is interposed longitudinally between the exhaust case and the exhaust cone and fastened to the exhaust case and to the annular inner wall. The assembly further includes elastic means configured to deform radially and prestressed radially between the annular outer wall and the connecting member.