A Perfect Cell Partitioning (PCP) scheme is described for controlling the transmission power of base stations in a cellular communication system to prevent radio frequency interference among adjacent base stations. A base station using this scheme can use its entire frequency range, while one using the conventional scheme can use only a quarter of it. Simulation and analytic results showed that the PCP scheme is more effective than the conventional one when the node density is lower than 6. However, the probability of successful communication is relatively low. A modified version of this scheme in which the base station sacrifices the nodes near its border has a significantly higher probability.