A turbine blade including an airfoil (31) extending above a platform (32) and a root (33) extending below the platform, the root of the blade having the form of a radially extending arm (34), being produced from composite material and including at least one cylindrical face (34). The direction of the generatrices which are oriented in the direction of the platform to allow a clamping piece (5) to slide towards the latter on the cylindrical face under the action of centrifugal force. The arm includes, at its lower end, a protuberance (35) forming a radial bearing point for engagement with an element for retaining the blade on a turbine disc (1). The root (33) is located entirely on the side of the protuberance with respect to the face.