A method for manufacturing a turbine engine blade (25) comprising a pressure side and a suction side separated from one another by an inner space for the circulation of cooling air, the blade (25) comprising a tip (S) with a closing wall (29) joining the pressure side and suction side walls in the region of this tip (S) in order to define a well shape, the closing wall including through-holes. The closing wall (29) obtained by moulding has a considerable nominal thickness with pits (36, 37) locally reducing this thickness at each through-hole in order to facilitate the removal by chemical etching of alumina rods defining the holes. Since the closing wall (29) thus has a large nominal thickness, it can then be machined in order to form raised patterns or complex shapes inside the well.