A method of making at least one rim (128; 228) situated at the free end (114; 214) of a rotor blade (110; 210) for a gas turbine engine, the method comprising the following steps: a) providing a blade (110; 210) presenting at least one base for a rim (128; 228) at its free end; b) providing a spray nozzle suitable for moving relative to said blade (110; 210), and a first source of a first powder material, and a second source of a second powder material, said first source and said second source being connected to the spray nozzle; c) providing a laser source connected to an optical head suitable for moving relative to said blade (110; 210) in order to focus the laser beam on a point of the surface of said base for a rim (128; 228); d) aiming the optical head and the nozzle on a common point of the surface of the top of the base for the rim (128; 228); e) activating the laser source and the sources (35; 45) of powder material so as to form a localized melt in the vicinity of said point, into which the powder material is injected, thereby forming a localized region of extra thickness; f) aiming the optical head and the nozzle on another point of the surface of the top of the base adjacent to said localized region of extra thickness and returning to step e) until a layer has been formed over substantially the entire width of the top of the base; and g) building at least a portion of said rim (128; 228) by depositing successive layers on the top of the base, each layer resulting from performing steps d) to f) and the following sub-steps: g1) forming two annular beads on the surface of the base for the rim (128; 228), using the second powder material or a mixture of said second material and said first material by causing the optical head and the nozzle to be offset during step f) in a longitudinal direction extending between the leading edge (120; 220) and the trailing edge (122; 222) relative to the previously-obtained localized region of extra thickness; and g2) filling a zone situated between the two annular beads with the first powder material. a) providing a blade (110; 210) presenting at least one base for a rim (128; 228) at its free end; b) providing a spray nozzle suitable for moving relative to said blade (110; 210), and a first source of a first powder material, and a second source of a second powder material, said first source and said second source being connected to the spray nozzle; c) providing a laser source connected to an optical head suitable for moving relative to said blade (110; 210) in order to focus the laser beam on a point of the surface of said base for a rim (128; 228); d) aiming the optical head and the nozzle on a common point of the surface of the top of the base for the rim (128; 228); e) activating the laser source and the sources (35; 45) of powder material so as to form a localized melt in the vicinity of said point, into which the powder material is injected, thereby forming a localized region of extra thickness; f) aiming the optical head and the nozzle on another point of the surface of the top of the base adjacent to said localized region of extra thickness and returning to step e) until a layer has been formed over substantially the entire width of the top of the base; and g) building at least a portion of said rim (128; 228) by depositing successive layers on the top of the base, each layer resulting from performing steps d) to f) and the following sub-steps: g1) forming two annular beads on the surface of the base for the rim (128; 228), using the second powder material or a mixture of said second material and said first material by causing the optical head and the nozzle to be offset during step f) in a longitudinal direction extending between the leading edge (120; 220) and the trailing edge (122; 222) relative to the previously-obtained localized region of extra thickness; and g2) filling a zone situated between the two annular beads with the first powder material. g1) forming two annular beads on the surface of the base for the rim (128; 228), using the second powder material or a mixture of said second material and said first material by causing the optical head and the nozzle to be offset during step f) in a longitudinal direction extending between the leading edge (120; 220) and the trailing edge (122; 222) relative to the previously-obtained localized region of extra thickness; and g2) filling a zone situated between the two annular beads with the first powder material.