In　this　article,　we　represent　a　new　numerical　method　for　solving　the　nonstationary　Navier-Stokes　equations　in　an　unbounded　domain.　The　technique　consists　of　coupling　the　boundary　integral　and　the　finite　element　method.　The　variational　formulation　and　the　well-posedness　of　the　coupling　method　are　obtained.　The　convergence　and　optimal　error　estimates　for　the　approximate　solution　are　provided.　(C)　1998　John　Wiley　&　Sons,　Inc.