In this paper, we propose a new formulation for solving the channel assignment problem for Multi-cell WLANs as a mixed integer linear programming (MILP) problem. The objective is to minimize the total interference seen by all Access Points (APs). The main advantage of the proposed algorithm is that it provides a global solution and at the same time guarantees non-overlapping channel assignment. The proposed channel assignment formulation can be used for different topologies of WLAN as demonstrated in the simulation. Simulation results show that the proposed algorithm outperforms the pick-first greedy algorithm and the single channel assignment method. The proposed channel assignment technique reduces the total interference at all APs which leads to an improved throughput.