NOVELTY - The method comprises mechanically reducing (110) an initial composite filament to produce an intermediate composite filament having a reduced cross sectional dimension, a core made from a first material and a cladding that is made from a second material and encloses the core, cutting (120) the intermediate composite filament into shorter filaments, inserting (130) the shorter composite filaments side by side into a first matrix made from a third material, and mechanically reducing (140) the first matrix with the shorter filaments.    USE - The method is useful for fabricating micro-sized composite filaments, which are useful in an electrode for an electrochemical cell and a hydrogen fuel cell, a catalytic converter for reducing pollutants in a flue gas and an ozone converter (all claimed), where the catalytic converter is an automotive catalytic converter useful in hybrid cars, and the ozone converter decomposes ozone in an intake air of a high-flying aircraft.    ADVANTAGE - The method is capable of economically fabricating the micro-sized composite filaments with improved mechanical strengths, increased thermal and electric conductance and high flexibility thus reducing weight and energy consumption of the ozone converter.    DETAILED DESCRIPTION - The method comprises mechanically reducing (110) an initial composite filament to produce an intermediate composite filament having a reduced cross sectional dimension, a core made from a first material and a cladding that is made from a second material and encloses the core, cutting (120) the intermediate composite filament into shorter filaments, inserting (130) the shorter composite filaments side by side into a first matrix made from a third material, mechanically reducing (140) the first matrix with the shorter filaments to further reduce the cross sectional dimensions of the shorter filaments, and isolating (150) the shorter filaments having further reduced cross sectional dimensions from the first matrix. The initial composite filament is obtained by inserting the core into a tube of the cladding and coating the core with a layer of the cladding. The first matrix has a tubular structure and cylindrical holes. The inserting step comprises inserting the shorter filaments as a bundle into the first matrix and inserting the shorter filaments into the cylindrical holes of the first matrix. The third material is the same as the first material. The method further comprises: annealing the initial composite filament before mechanically reducing the initial filament; cutting the mechanically reduced first matrix with the shorter filaments embedded within the first matrix into composite structures; inserting the composite structures into a second matrix made from a fourth material; mechanically reducing the second matrix with the composite structures; and forming an array of filamentary structures from the mechanically reduced matrix with the shorter filaments. The isolating step comprises chemical etching the first matrix material. The initial composite filament includes a compatibility layer positioned between the core and the cladding. A cladding of the shorter filaments having further reduced cross sectional dimension (less than 2 micron) has a thickness of less than 10 nm. The step of forming the array of filamentary structures comprises weaving and adding reinforcing fibers. The initial composite filament includes initial filaments that include filaments having different compositions or sizes. The initial composite filament includes an outer layer made from the fourth material in contact with the cladding. The fourth material is a same material as the third material. An INDEPENDENT CLAIM is included for a composite filament.    DESCRIPTION OF DRAWING(S) - The diagram shows a flow diagram of a process for fabricating composite filaments.    Reducing an initial composite filament to produce intermediate composite filament (110)    Cutting the intermediate composite filament into shorter filaments (120)    Inserting the shorter composite filaments side by side into a first matrix made from a third material (130)    Mechanically reducing the first matrix with the shorter filaments to further reduce the cross sectional dimensions of the shorter filaments (140)    Isolating the shorter filaments having further reduced cross sectional dimensions from the first matrix. (150)