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A novel scheme to reduce transverse beam emittance in a ring accelerator is proposed by using a pair of coupling cavities as a basic unit to control damping partition numbers. As indicated by Robinson in 1958, a simple rf electromagnetic field (e.g., a TM210 mode by a single coupling cavity) cannot control the damping partition of three eigenoscillation modes in a ring accelerator due to the cancellation between the contributions from the magnetic and electric fields. Based on both analytical and numerical studies, we show that a pair of coupling cavities that satisfy phase and optics matching conditions can overcome this cancellation. The results indicate that the horizontal emittance is reducible to the theoretical limit based on the steady state condition and also, the emittance is reducible below the reduction limit under a nonsteady state by driving the coupling cavities with gated signals. [ABSTRACT FROM AUTHOR]