A method for making a fine carbon-fibre microelectrode is suggested here. The diameter of the recording tip of the proposed microelectrode at the borderline of glass insulation is 2-4 microm. The method uses tapering and trimming the tip of a factory-made carbon-fibre with pulsed electric current. The treated fibre is introduced into a glass micropipette of desired parameters and is fixed in it. The proposed microelectrodes have good characteristics for extracellular recording of action and synaptic potentials. The fine tip of the microelectrode can pick out a firing activity of a small single unit better and injures the nerve tissue less in comparison with the ordinary carbon-fibre microelectrode.