Due to insufficient available bandwidth resources and the continuously growing demand for cellular communication services, the channel assignment problem has become increasingly important. To trace the optimal assignment, several heuristic strategies have been proposed. So far, most of them focus on the small-scale systems containing no more than 25 cells and they use an anachronistic cost model, which does not satisfy the requirements of most existing cellular operators, to measure the solution quality. Solving the small-scale channel assignment problems could not be applied into existing large scale cellular networks' practice. This article proposes a decomposition approach to solve the fixed channel assignment problem (FCAP) for large-scale cellular networks through partitioning the whole cellular network into several smaller sub-networks and then designing a sequential branch-and-bound algorithm that is made to solve the FCAP for them sequentially. The key issue of partition is to minimize the dependences of the sub-networks so that the proposed heuristics for solving smaller problems will suffer fewer constraints in searching for better assignments. The proposed algorithms perform well based on experimental results and they were applied to the Taiwan Cellular Cooperation (TCC) in ChungLi city to find better assignments for its network.