To further suppress the multiple-access interference (MAI) in frequency-hopping multiple-access (FHMA) system, a novel kind of FH sequence set named as no-hit-zone (NHZ) sequence, is proposed for an FHMA system with M-ary FSK modulation (MFSK/FHMA) in this paper. Expressions for the decision variables are derived for the asynchronous MFSK/FHMA system with NHZ sequence set (MFSK/FHMA-NHZ) under a slow Rayleigh-fading channel model. For the special case of M=2, accurate analytic bit error rate (BER) is derived as a function of maximum relative delay D and the number of users K by a characteristic function method. The theoretical results validated by Monte Carlo simulations are used to investigate the dependence of the average BER on D and K. Comparison with the MFSK/FHMA system with Markov hit pattern (MFSK/FHMA-Markov) shows that MFSK/FHMA-NHZ system performs better than Markov hit pattern system as long as D is restricted in a certain range and further, the gain in the performance increases with increase in the value of K.