In this paper, we consider a lattice of the coupled logistic map with periodic boundary conditions. We prove that synchronization occurs in the one-dimensional lattice with lattice size n = 4 for any γ in the chaotic regime [γ∞ ≈ 3.57, 4]. It is worthwhile to emphasize that, despite of the fact that there is a rigorous proof for synchronization in many systems with continuous time, almost nothing is rigorously proved for the systems with discrete time.