An annular wall of a combustion chamber of a turbine engine including: a cold side and a hot side; plural dilution holes to allow circulating air of the cold side to enter the hot side for dilution of an air/fuel mixture; plural cooling orifices to allow the circulating air of the cold side to enter the hot side to form a film of cooling air along the annular wall, the cooling orifices distributed spaced axially from one another and with geometric axes inclined, in an axial direction of flow of combustion gases, by an inclination angle relative to a normal to the annular wall; plural additional cooling orifices arranged directly downstream of the dilution holes and distributed spaced axially from one another, with geometric axes arranged in a plane perpendicular to the axial direction and inclined by an angle of inclination relative to a normal to the annular wall.