Method for finishing the shape of a turbine engine blade by machining, in which at least one area is produced thicker than the required profile, the said thickened portion forming a first surface with the surrounding profile, the machining of the method being aimed at removing this thickened portion, using a suitable tool, to obtain a third surface, the theoretical profile of the component being moreover defined by a second surface, characterised in that it comprises the following steps to define the position of the bit of the said tool during machining of the said area: - defining, on the second surface, a grid formed by intersecting lines forming nodes and delimiting squares, the said grid covering the area to be machined and extending so that the outer limit of the machining area is completely enclosed within the outer limits of the grid, - defining the position of each point of contact between the component and the tool for machining along the theoretical profile, by weighting with reference to the position of the nodes (Ni) of the square in which it is located, - measuring, for each node Ni located outside the outer limit, the delta(Ni) between the first surface at said node and the theoretical position of the node on the second surface, the said difference being measured normal to the second surface, - calculating, step by step, the differences delta(Nj) for each node Nj located within the outer limit, by selecting the square to which said node belongs and for which the delta(Ni) or delta(Nj) differences of the other nodes are already known, and interpolating from the said delta(Ni) or delta(Nj) differences, weighted according to the length of the segments connecting the said nodes, - defining the delta to be applied to each point P to obtain a point of contact P' between the component and the tool, relative to the reference input into the machine tool, by the weighted sum of the deltas(Ni) of the nodes of the square to which the said point P belongs, using the said weighting performed with reference to the nodes N(i). - defining, on the second surface, a grid formed by intersecting lines forming nodes and delimiting squares, the said grid covering the area to be machined and extending so that the outer limit of the machining area is completely enclosed within the outer limits of the grid, - defining the position of each point of contact between the component and the tool for machining along the theoretical profile, by weighting with reference to the position of the nodes (Ni) of the square in which it is located, - measuring, for each node Ni located outside the outer limit, the delta(Ni) between the first surface at said node and the theoretical position of the node on the second surface, the said difference being measured normal to the second surface, - calculating, step by step, the differences delta(Nj) for each node Nj located within the outer limit, by selecting the square to which said node belongs and for which the delta(Ni) or delta(Nj) differences of the other nodes are already known, and interpolating from the said delta(Ni) or delta(Nj) differences, weighted according to the length of the segments connecting the said nodes, - defining the delta to be applied to each point P to obtain a point of contact P' between the component and the tool, relative to the reference input into the machine tool, by the weighted sum of the deltas(Ni) of the nodes of the square to which the said point P belongs, using the said weighting performed with reference to the nodes N(i).