In order to find out what might be the mechanism to drive the inter-decadal oscillation of the climate system,the spatial features of unstable coupled waves in the mid-latitude air-sea system are investigated on the basis of the simple air-sea coupled model which includes the deep ocean effects.Results show that: for the unstable coupled waves in the air-sea system,the air disturbance wave goes ahead of the sea disturbance wave by 0 to π/2 in the phase,and especially when the phase difference is π/4,this special spatial structure can cause the most unstable air-sea interaction;in the coupled system,the amplitude relation between the air and sea disturbance waves is determined by the relative size of wind stress and ocean heating coefficients.The amplitude of air disturbance may be larger or smaller than that of sea disturbance;and the deep ocean coefficient brings little change to the spatial structure of the air-sea couple waves.