Method of cutting a metal component, implementing a plasma cutting torch for an arc supplied with assistance gas, said method comprising the following successive steps: a) positioning the lower end of the torch at a given transfer height (H 1), in relation to the upper surface of the metal component to be cut, the transfer of an electric arc towards said component, and the production of a plasma arc by ionisation of the assistance gas by means of the transferred electric arc, b) translation movement of the torch in relation to the metal component to be cut at a given first speed (V 1), with V 1 >V c, and the start of the piercing of said component by means of the plasma from the arc produced in step a), the lower end of the torch being separated from the upper surface of the metal component to be cut up to the given first height (H 1), with H 1 >H t, d) translation movement of the torch in relation to the metal component to be cut at a given first cutting speed (V c), and the start of the cutting of the said component according to a given cutting trajectory, by means of the plasma from the arc produced in step a), characterised in that, previously to step d), said method furthermore comprises the following step: c) translation movement of the torch in relation to the metal component to be cut, in other words, in a parallel plane to the surface of the said component, at a given non-zero second speed (V 2), with V 2 <V 1, and the end of the piercing of the said component, the lower end of the torch being aligned with the upper surface of the component, up to a given second height (H 2), with H 2 <H 1, the height movement and movement bringing the torch closer being carried out simultaneously to the translation movement of the torch, and during at least one part of the translation movement step. a) positioning the lower end of the torch at a given transfer height (H 1), in relation to the upper surface of the metal component to be cut, the transfer of an electric arc towards said component, and the production of a plasma arc by ionisation of the assistance gas by means of the transferred electric arc, b) translation movement of the torch in relation to the metal component to be cut at a given first speed (V 1), with V 1 >V c, and the start of the piercing of said component by means of the plasma from the arc produced in step a), the lower end of the torch being separated from the upper surface of the metal component to be cut up to the given first height (H 1), with H 1 >H t, d) translation movement of the torch in relation to the metal component to be cut at a given first cutting speed (V c), and the start of the cutting of the said component according to a given cutting trajectory, by means of the plasma from the arc produced in step a), c) translation movement of the torch in relation to the metal component to be cut, in other words, in a parallel plane to the surface of the said component, at a given non-zero second speed (V 2), with V 2 <V 1, and the end of the piercing of the said component, the lower end of the torch being aligned with the upper surface of the component, up to a given second height (H 2), with H 2 <H 1, the height movement and movement bringing the torch closer being carried out simultaneously to the translation movement of the torch, and during at least one part of the translation movement step.