A　full　discrete　two-level　postprocessing　Fourier　Galerkin　scheme　for　the　unsteady　Navier-Stokes　equations　with　a　periodic　boundary　condition　is　proposed　in　this　paper.　By　de.　ning　a　new　projection,　the　interaction　between　the　large　and　small　eddies　is　reflected　by　the　associated　space　splitting　to　some　extent.　Therefore,　a　weakly　coupled　system　of　the　large　and　small　eddies　is　obtained.　Stability　and　error　estimates　for　the　weakly　coupled　two-level　scheme　are　established　in　the　paper.　The　proposed　scheme　is　an　effective　algorithm　because　nonlinearity　is　treated　only　in　the　coarse-level　subspace　by　solving　the　coarse-level　standard　Galerkin　equation,　and　the　matrix　of　the　linear　algebraic　equations　arising　in　each　fine-level　time　stepping　is　a　sparse　matrix,　especially　for　large　scale　computations.　As　a　result,　the　new　scheme　saves　a　lot　of　CPU　time　and　memory　in　comparison　with　the　standard　Fourier　Galerkin　method　for　deriving　an　approximation　of　prescribed　accuracy.