A wall in which there is formed at least one cooling channel, said wall being cooled by cool air flowing in the channel, the channel comprising a hole and a diffusion portion, the hole opening out at one end into the inside surface of the wall, and at its other end into the diffusion portion where it forms an orifice, the diffusion portion flaring around said orifice and opening out into the outside surface of the wall, the diffusion portion having a bottom whose front end is substantially plane, sloping, and extending in front of the orifice, and also having a margin extending behind, round the sides, and in front of the orifice, said margin joining the sides of the front end. A method and an electrode for making such a cooling channel. A turbomachine blade presenting such a wall.