A　new　stabilized　finite　element　method　is　considered　for　the　time-dependent　Stokes　problem,　based　on　the　lowest-order　P(1)　-　P(0)　and　Q(1)　-　P(0)　elements　that　do　not　satisfy　the　discrete　inf-sup　condition.　The　new　stabilized　method　is　characterized　by　the　features　that　it　does　not　require　approximation　of　the　pressure　derivatives,　specification　of　mesh-dependent　parameters　and　edge-based　data　structures,　always　leads　to　symmetric　linear　systems　and　hence　can　be　applied　to　existing　codes　with　a　little　additional　effort.　The　stability　of　the　method　is　derived　under　some　regularity　assumptions.　Error　estimates　for　the　approximate　velocity　and　pressure　are　obtained　by　applying　the　technique　of　the　Gaterkin　finite　element　method.　Some　numerical　results　are　also　given,　which　show　that　the　new　stabilized　method　is　highly　efficient　for　the　time-dependent　Stokes　problem.　Copyright　(C)　2009　John　Wiley　&　Sons,　Ltd.