The invention relates to an assembly for a turbine of a turbomachine with a longitudinal axis (X) comprising:



an exhaust cone (100) comprising an outer annular wall (102) for the flow of a primary airflow and an annular box arranged radially inside said outer annular wall (102), the annular box comprising an inner annular wall (104) arranged radially inside the outer annular wall of the exhaust cone,
an exhaust case arranged upstream of the exhaust cone, and
a connecting member (106) flexible in a radial direction, interposed longitudinally between the exhaust case and the exhaust cone (100), the connecting member being fastened to the exhaust case and to the inner annular wall (104), and
wherein the inner annular wall (104) is connected to the outer annular wall (102) by fastening means (112) configured to enable movements of the inner annular wall (104) in a circumferential direction and a longitudinal direction with respect to the outer annular wall (102).