Abstract: The matrix of the composite material is made in sequenced manner by chemical vapor infiltration within fiber reinforcement. Each elementary sequence of the matrix comprises a relatively flexible layer and a relatively rigid ceramic layer, and the sequences are of thicknesses that increase going away from the reinforcing fibers, with the thickness at least of the first-deposited sequence being selected to be sufficiently small for the fibers to be coated in essentially individual manner. The flexible layers are made of an anisotropic material having sufficient capacity for elastic deformation in shear and transversely, and although a mainly ceramic character is conserved for the matrix, the thickness of the flexible layers is nevertheless selected to be sufficiently large to be capable of absorbing differential expansion of the components of the composite material while it is being made without inducing the existence of an initial network of cracks.