A method for manufacturing a turbine engine blade including an airfoil with a profile defined by a theoretical digital model, the method including: manufacturing a blank having a thickened portion along a trailing edge of the airfoil relative to the theoretical profile; removing the thickened portion by adaptive machining, including: positioning the blank in a reference frame; acquiring, by probing at a predetermined number of points on a first surface of the blank along the trailing edge, positions of the points in the reference frame; determining differences, in one direction, in position from corresponding points of the theoretical model; producing machining grids on the blank surface, peaks of the grids determined from the points; determining an amount of material to be removed from the surface of the grids, based on the position of the points relative to the peaks and the deviations in position; and machining the airfoil.