Bilirubin oxidase (BOD) was immobilized as a multiple layer in a cationic polymer (poly-L-lysine) matrix on an electrode surface. The BOD-modified electrode catalyzed four-electron reduction of dioxygen (O-2) to water, without any mediator, to produce a diffusion-controlled voltammogram for the O-2 reduction in a quiescent solution. The voltammogram was successfully analyzed by the theory of irreversible voltammograms. Under convective conditions where O-2 depletion was negligible near the electrode surface, a steady-state voltammogram was obtained with a limiting current density of about 1 mA cm(-2). The steady-state voltammogram was explained by an equation derived on the basis of a reaction layer model, in which BOD was considered to be diffusible in the immobilized layer. (C) 2004 Elsevier B.V. All rights reserved.