Startinig from the quasi-geostrophic barotropic vorticity equation .a new bi-time scale scheme is proposed and obtained for the first time are the coupled equtions of 4-wavequasi-resonance for the barotropic wave motion .i. c.. the Landau equations in a broad sense .And with the aid of new conservative quantities. the very low frequency periodic solution of the equations is found with the period of about one year. This can be regarded as a new phys-ical mechanism of interannual oscillation in the real atmosphere. Besides. the wave vectors of 4-wave quasi-resonance are also obtained in this paper.