The role of inhibitory self-connection in a second order recurrent neural network with delays has been investigated. A sufficient condition is proposed to guarantee the global asymptotical stability of the equilibrium point for the delayed neural network. The results indicate that an unstable neural network without inhibitory interconnections can be asymptotically stabilized to a unique equilibrium point via embedding inhibitory self-connections with proper strengths, and the role of inhibitory self-connections will be restricted by the magnitude of transmission delays. Two simulation examples are used to show the effectiveness of the obtained result.