A sectorized nozzle for a turbomachine, the nozzle being made up of cylindrical sectors and comprising two annular platforms interconnected by substantially radial vanes, together with an annular rail for supporting elements of abradable material, each inner platform having longitudinally-extending edges that are V-shaped, and each rail sector having, on at least one of its sides, means for bearing axially on corresponding means provided on an adjacent nozzle sector.