A turbine blade for a turbojet engine, made of a ceramic matrix composite material and including a vane that extends above a platform and a root that extends below the platform is provided. The pressure face and the suction face of the vane is formed by sheets of a composite material, the sheets meeting at the leading edge and trailing edge of the vane. The pressure face and suction face are formed by the same sheet bent back on itself, in a radial direction, at the leading edge or trailing edge.