The method comprises the steps of: forming a porous fiber-reinforcing structure; introducing into the pores of the fiber structure powders containing elements for constituting the composite material matrix; and forming at least a main fraction of the matrix from said powders by causing a reaction to take place between said powders or between at least a portion of said powders and at least one delivered additional element; the powders introduced into the fiber structure and the delivered additional element(s) comprising elements that form at least one healing discontinuous matrix phase including a boron compound and at least one discontinuous matrix phase including a crack-deflecting compound of lamellar structure. At least a main fraction of the matrix is formed by chemical reaction between the powders introduced into the fiber structure and at least one delivered additional element, or by sintering the powders.