It is shown analytically as well as numerically that a periodic window of the coupled map system exists only for very weak coupling strength (about 10-3 for period 3 window, for instance), which could be defined as the depth of the window. Within the windows the behavior of the coupled map system could be recovered by dealing with a few number of modes, which consist of coupled three maps. The first Lyapunov exponent for the coupled map system shows a "zigzag" curve form virsus the coupling strength.