A composite material turbine nozzle blade including an airfoil adapted to have a cooling fluid flow through it and extending between a shroud and a root is provided. The shroud is shaped to be attached to one or more turbine casings of a turbomachine and the root is shaped to provide a junction with a turbine internal casing. The root is produced with a loosened texture and includes an external upstream side loosened texture lug and an external downstream side loosened texture lug. The ends of the two external side lugs extend radially relative to the rotation axis of the turbomachine to form a device for supporting and centering the internal casing.