An assembly for a turbomachine with a longitudinal axis having an exhaust cone with an outer annular wall for the flow of a primary airflow and an annular box arranged radially inside the outer annular wall, an exhaust casing arranged upstream of and connected to the exhaust cone. One end of the outer annular wall or one end of the annular box may be free to move relative to and have no mechanical connection with the exhaust cone or the exhaust casing.