In a simple coupled-map system, we show that the desynchronization of the chaotic attractor occurs through a series of Hopf bifurcations. As a result of the accumulation of these processes, the blowout bifurcation of this coupled map system is a new kind of Hopf bifurcation from a chaotic attractor. Riddling, bubbling, and characters of this particular manifestation of Hopf bifurcation from a chaotic attractor are studied in this paper.