The largest Lyapunov exponent and the Lyapunov spectrum of a coupled map lattice are studied when the system state is desynchronous chaos. In the large system size limit a scaling region is found in the parameter space where the largest Lyapunov exponent is independent of the system size and the coupling strength. Some scaling relation between the Lyapunov spectrum distributions for different coupling strengths is found when the coupling strengths are taken in the scaling parameter region. The existence of the scaling domain and the scaling relation of Lyapunov spectra there are heuristically explained.