In　this　paper,　we　propose　and　study　a　new　local　stabilized　nonconforming　finite　method　based　on　two　local　Gauss　integrations　for　the　two-dimensional　Stokes　equations.　The　nonconforming　method　uses　the　lowest　equal-order　pair　of　mixed　finite　elements　(i.e.,　NCP(1)-P(1)).　After　a　stability　condition　is　shown　for　this　stabilized　method,　its　optimal-order　error　estimates　are　obtained.　In　addition,　numerical　experiments　to　confirm　the　theoretical　results　are　presented.　Compared　with　some　classical,　closely　related　mixed　finite　element　pairs,　the　results　of　the　present　NCP(1)-P(1)　mixed　finite　element　pair　show　its　better　performance　than　others.