A method of depositing a coating of a first metal alloy on a fiber extending in a main direction D, the method comprising the following steps: a) providing a first mass of a first metal alloy and heating said first mass to above its melting temperature so that this alloy is in the liquid state and occupies a space E1; the first metal alloy is the Ti-6242 titanium alloy having the following composition by weight 6%Al + 2%Sn + 4%Zn + 2%Mo, the balance being Ti, b) causing said fiber to move in translation from upstream to downstream through said liquid first mass along the direction in which said fiber extends at a first speed V1, faster than 2 m/s, such that said fiber becomes covered over at least a portion of its length by a coating of said first alloy, which coating presents a non-zero thickness over the entire periphery of the fiber in a plane perpendicular to said main direction D, which method is characterized in that, prior to step a), the following steps are performed: i) providing a second mass of a second metal alloy having a melting temperature T F2 that is strictly higher than the melting temperature T F1 of said first alloy, the second metal alloy is a titanium niobium alloy (Ti-Nb) comprising 51% by weight of Ti and 49% by weight of Nb; j) heating said second mass to above its melting temperature so that the second alloy is in the liquid state and occupies a space E2, and then moving said fiber in translation from upstream to downstream through said second alloy, this translation taking place at a second speed V2, equal to 1 m/s or slower, which is such that the condition under which the second alloy is taken up during this translation lies under visco-capillary conditions, such that the fiber becomes covered, over said portion of its length, by a coating of said second alloy, which coating presents a non-zero thickness over the entire periphery of the fiber; and k) cooling said coating of the second alloy until it becomes solid. a) providing a first mass of a first metal alloy and heating said first mass to above its melting temperature so that this alloy is in the liquid state and occupies a space E1; the first metal alloy is the Ti-6242 titanium alloy having the following composition by weight 6%Al + 2%Sn + 4%Zn + 2%Mo, the balance being Ti, b) causing said fiber to move in translation from upstream to downstream through said liquid first mass along the direction in which said fiber extends at a first speed V1, faster than 2 m/s, such that said fiber becomes covered over at least a portion of its length by a coating of said first alloy, which coating presents a non-zero thickness over the entire periphery of the fiber in a plane perpendicular to said main direction D, i) providing a second mass of a second metal alloy having a melting temperature T F2 that is strictly higher than the melting temperature T F1 of said first alloy, the second metal alloy is a titanium niobium alloy (Ti-Nb) comprising 51% by weight of Ti and 49% by weight of Nb; j) heating said second mass to above its melting temperature so that the second alloy is in the liquid state and occupies a space E2, and then moving said fiber in translation from upstream to downstream through said second alloy, this translation taking place at a second speed V2, equal to 1 m/s or slower, which is such that the condition under which the second alloy is taken up during this translation lies under visco-capillary conditions, such that the fiber becomes covered, over said portion of its length, by a coating of said second alloy, which coating presents a non-zero thickness over the entire periphery of the fiber; and k) cooling said coating of the second alloy until it becomes solid.