A chaotic synchronized system of two coupled skew tent maps is discussed in this paper. The locally and globallyriddled basins of the chaotic synchronized attractor are studied. It is found that there is a novel phenomenon in thelocal-global riddling bifurcation of the attractive basin of the chaotic synchronized attractor in some specific couplingintervals. The coupling parameter corresponding to the locally riddled basin has a single value which is embeddedin the coupling parameter interval corresponding to the globally riddled basin, just like a breakpoint. Also, there isno relation between this phenomenon and the form of the chaotic synchronized attractor. This phenomenon is foundanalytically. We also try to explain it in a physical sense. It may be that the chaotic synchronized attractor is in thecritical state, as it is infinitely close to the boundary of its attractive basin. We conjecture that this isolated criticalvalue phenomenon will be common in a system with a chaotic attractor in the critical state, in spite of the system beingdiscrete or differential.