A new algorithm for frequency channel assignment in high capacity cellular mobile communication systems is proposed. The algorithm is the advanced type of the fixed channel assignment scheme. It enables calls having all nominal channels busy to be served by adjacent cells have idle channels. Thus, it considerably reduces the blocking probability compared with the fixed channel assignment. Simulation has been performed for a 49-cell system having uniform traffic density hexagonal array as a representative system lay out. Results showed that new algorithm is better than the fixed channel assignment scheme in high capacity cellular mobile communication systems.