A cooled turbine blade for a gas turbine engine including a pressure surface wall, a suction surface wall and a distal wall connecting the pressure surface wall and the suction surface wall, arranged so as to create in the region of the distal end of the blade at least one external cavity forming a bathtub-shaped cavity and at least one internal cavity separated by the distal wall, the blade having at least one opening for the introduction of a flow of cooling air into the external cavity, wherein, on the one hand, at least one part of the distal wall is inclined relative to the verticals of the pressure surface wall and, on the other hand, the opening is created in the vicinity of the distal wall so that the flow of cooling air is directed towards the distal end of the pressure surface wall.