A　fully　discrete　penalty　finite　volume　method　is　introduced　for　the　discretization　of　the　two-dimensional　transient　Navier-Stokes　equations.　where　the　temporal　discretization　is　based　oil　a　backward　Euler　scheme　and　the　spatial　discretization　is　based　on　a　finite　volume　scheme　that　uses　a　pair　of　P-2-P-0　trial　functions　oil　triangles.　This　method　allows　us　to　efficiently　separate　the　computation　of　velocity　from　that　of　pressure　With　reasonably　large　time　steps.　and　conserves　mass　locally.　In　addition,　error　estimates　of　optimal　order　are　obtained　for　the　fully　discrete　method　under　reasonable　assumptions　oil　temporal　and　spatial　step　sizes　and　the　physical　data.　Finally.　we　present　two　numerical　examples　to　illustrate　file　numerical　algorithims　developed　and　to　show　numerical　results　that　agree　with　the　theory　established.　(C)　2007　IMACS.　Published　by　Elsevier　B.V.　All　rights　reserved.