For　nonsymmetric　saddle　point　problems　arising　from　the　steady　Navier-Stokes　equations,　Pan,　Ng　and　Bai　presented　a　deteriorated　positive-definite　and　skew-Hermitian　splitting　(DPSS)　preconditioner　(Pan　et　al.,　2006)　to　accelerate　the　convergence　rates　of　the　Krylov　subspace　iteration　methods　such　as　GMRES.　In　this　paper,　the　unconditional　convergence　property　of　the　DPSS　iteration　method　is　proved　and　a　relaxed　DPSS　(RDPSS)　preconditioner　is　proposed.　The　RDPSS　preconditioner　is　much　closer　to　the　coefficient　matrix　than　the　DPSS　preconditioner　in　certain　norm,　which　straightforwardly　results　in　an　RDPSS　iteration　method.　The　convergence　conditions　of　the　RDPSS　iteration　are　analyzed　and　the　optimal　parameter,　which　minimizes　the　spectral　radius　of　the　RDPSS　iteration　matrix,　is　derived.　Using　the　RDPSS　preconditioner　to　accelerate　some　Krylov　subspace　methods　(like　GMRES)　is　also　studied.　The　eigenproperty　of　the　preconditioned　matrix　is　described　and　an　upper　bound　of　the　degree　of　the　minimal　polynomial　of　the　preconditioned　matrix　is　obtained.　Finally,　numerical　experiments　of　a　model　Navier-Stokes　equation　are　presented　to　illustrate　the　efficiency　of　the　RDPSS　preconditioner.　(C)　2014　Elsevier　B.V.　All　rights　reserved.