The present invention relates to a turbine ring assembly including a plurality of ring sectors (1) made of a composite material having a ceramic matrix forming a turbine ring, and a ring-supporting structure (2) including two annular flanges (11a; 11b) between which an attachment portion (9) of each ring sector is held, the annular flanges of the ring-supporting structure each having at least two angled portions (12a; 12b; 13a; 13b) resting on the attachment portions of the ring sectors, said angled portions forming, when viewed in a meridian cross-section, an angle other than zero relative to the radial direction (R) and to the axial direction (A).