A method of fabricating a part out of composite material comprising fiber reinforcement densified by a metal matrix, the method comprising at least the following steps: a) positioning a plurality of fibers (10; 10') comprising a core (10a; 10'a) made of ceramic material coated by a metal sheath (10b; 10'b) on a first preform (7a; 27a; 37a) for a first portion of the part to be fabricated, said first preform (7a; 27a; 37a) comprising at least a metal powder of a first alloy and a first binder; b) positioning a second preform (7b; 27b; 37b) for a second portion of the part to be fabricated on the first preform (7a; 27a; 37a) in order to obtain a stack structure, the fibers (10; 10') being present between the first preform (7a; 27a; 37a) and the second preform (7b; 27b; 37b) in said stack structure, said second preform (7b; 27b; 37b) comprising at least a metal powder of a second alloy and a second binder, the melting temperature T 1 of the first alloy, the melting temperature T 2 of the second alloy, and the melting temperature T 3 of the metal sheath (10b; 10'b) of the fibers (10; 10') satisfying the following two conditions: |T 3 - T 1 |/T 1 ≤ 25%, and |T 3 - T 2 |/T 2 ≤ 25%, the melting temperatures T 1, T 2 and T 3 being expressed in degrees Celsius; c) eliminating the first and second binders present in the stack structure obtained after performing step b) in order to obtain a debindered stack structure; and d) heat treating the debindered stack structure in order to obtain the composite material part wherein the metal sheath (10b; 10'b) of the fibers (10; 10') is assembled with the powders of the first and second alloys by diffusion welding and wherein the powders of the first and second alloys are sintered in order to form the metal matrix. a) positioning a plurality of fibers (10; 10') comprising a core (10a; 10'a) made of ceramic material coated by a metal sheath (10b; 10'b) on a first preform (7a; 27a; 37a) for a first portion of the part to be fabricated, said first preform (7a; 27a; 37a) comprising at least a metal powder of a first alloy and a first binder; b) positioning a second preform (7b; 27b; 37b) for a second portion of the part to be fabricated on the first preform (7a; 27a; 37a) in order to obtain a stack structure, the fibers (10; 10') being present between the first preform (7a; 27a; 37a) and the second preform (7b; 27b; 37b) in said stack structure, said second preform (7b; 27b; 37b) comprising at least a metal powder of a second alloy and a second binder, the melting temperature T 1 of the first alloy, the melting temperature T 2 of the second alloy, and the melting temperature T 3 of the metal sheath (10b; 10'b) of the fibers (10; 10') satisfying the following two conditions: |T 3 - T 1 |/T 1 ≤ 25%, and |T 3 - T 2 |/T 2 ≤ 25%, the melting temperatures T 1, T 2 and T 3 being expressed in degrees Celsius; c) eliminating the first and second binders present in the stack structure obtained after performing step b) in order to obtain a debindered stack structure; and d) heat treating the debindered stack structure in order to obtain the composite material part wherein the metal sheath (10b; 10'b) of the fibers (10; 10') is assembled with the powders of the first and second alloys by diffusion welding and wherein the powders of the first and second alloys are sintered in order to form the metal matrix.