In real systems, because of the inevitable noise, a chaotic synchronized attractor A will turn into a metastable attractor A′ with an average lifetime . We analyze a two-dimensional coupled map with additive noises and find analytica lly that the riddled basin of A′ will disappear when >2T, where T is the duration of an experiment. Acc ording to the characters of the riddled basin without noises, it is found that t he riddled basin will turn into not only a temporal riddled basin but also a reg ular fractal basin. This result is universal in two-dimensional coupled chaotic synchronized maps, and the further numerical calculations can also confirm this point.