A sectorized nozzle for a turbine engine turbine including an inner sectorized annular platform and an outer sectorized annular platform connected together by radial airfoils, at least one of the platforms including a plurality of orifices for passing air in a neighborhood of its upstream end, the orifices being distributed over the circumference of the platform and opening out at their ends remote from the airfoils into a circumferential annular cavity of the sector of the platform, which cavity is closed by a metal sheet fastened to the platform sector and pierced by orifices for feeding cooling air.