New family of frequency hopping patterns with long period and good Hamming autocorrelation and Hamming crosscorrelation properties which can be used for frequency hopped multiple access communication systems is introduced. Period of frequency hopping patterns is qk-1, the alphabet size of frequency hopping patterns is q, and the size of family of frequency hopping patterns is q, where k is arbitrary integer and q is power of prime number. The maximum value of out-of-Phase Hamming autocorrelation function of any frequency hopping pattern and Hamming crosscorrelation function of any two frequency hopping patterns in the family is qk-1, which corresponds to optima1 Hamming correlation properties. And the average number of hits per q*q square in one frequency hopping pattern and its time shifted version or two frequency hopping patterns in the frequency hopped multiple access communication systems is less than 1.