In　real　systems,　because　of　the　inevitable　noise,　a　chaotic　synchronized　attractor　A　will　turn　into　a　metastable　attractor　A＇　with　an　average　lifetime　＜τ＞.　We　analyze　a　two-dimensional　coupled　map　with　additive　noises　and　find　analytically　that　the　riddled　basin　of　A＇　will　disappear　when　＜τ＞　＜　2　T　and　can　only　be　observed　qualitatively　when　＜tau＞　＞　2　T,　where　T　is　the　duration　of　an　experiment.　According　to　the　characters　of　the　riddled　basin　without　noises,　it　is　found　that　the　riddled　basin　will　turn　into　not　only　a　temporal　riddled　basin　but　also　a　regular　fractal　basin.　This　result　is　universal　in　two-dimensional　coupled　chaotic　synchronized　maps,　and　the　further　numerical　calculations　can　also　confirm　this　point.