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In this paper, the problem of assigning channels to calls in a cellular mobile communication by finding the minimum number of channels required to obtain an interference-free assignment, is considered. To speed up the results and getting interference free assignments the technique of increasing the co-site interference depending upon the adjacent channels interferences is used. This gives better results that the previous algorithms in this channel assignment. This heuristic algorithm is tested with many benchmark problems like Cellular Radio and Cellular Mobile Problem, and achieved better results in both types of problems and hence proved that the algorithm is efficient in giving results . We also compared the results with 12 Channel assignment problems (CAPs) used by previous researchers, and found our results better in efficiency. This research work can be effectively used in today's mobile systems.