Abstract: A method for manufacturing a part by forging, including producing a semifinished part by precision forging and polishing the part by an abrasive strip, compliant geometric characteristics of the part to be obtained being predetermined in a theoretical model. The method includes: measuring the geometrical characteristics of the semifinished part after the forging operations and comparing the characteristics with the theoretical model; determining noncompliant areas on the surface of the part; determining the amount of material to be removed from each noncompliant area to make the area compliant; and polishing the part using the abrasive strip, controlling the strip so as to remove the amount of material from each noncompliant area. The method can be used for example for polishing turbine engine fan blades.