A method for manufacturing a part made of composite material includes forming a ceramic matrix phase in pores of a fibrous preform by pyrolysis of a cross-linked copolymer ceramic precursor, the cross-linked copolymer including a first precursor macromolecular chain of a first ceramic having free carbon, and a second precursor macromolecular chain of a second ceramic having free silicon, the first macromolecular chain being bonded to the second macromolecular chain by cross-linking bridges including a bonding structure of formula *1—X—*2; in this formula, X designates boron or aluminium, -*1 designates the bond to the first macromolecular chain and -*2 the bond to the second macromolecular chain.