Based on the basic principle that the magnitudes and the frequencies of the regionally seismic activity within certain time duration（lgN=a-bM

G-R law） in seismological research

we find that the relationship between magnitude and frequency deviates from G-R law

even does not necessarily obey the G-R law through the research of the rock fracture experiments and strong seismic events in North China due to the effects of nonlinear deformation of rocks before the period of rocks’ instability.The Magnitude-Frequency’s deviation of small earthquakes in the region from the G-R law before strong earthquakes can be served as a precursor for strong earthquakes.This precursor may play an important role in the research of earthquake prediction.