In order to test the hypothesis that the fmax of large earthquakes is due to the source effect and is casually related to the corner frequency of small earthquakes when it becomes constant below magnitude about 3, we constructed the frequency-magnitude relation for earthquakes with magnitude range from -1/3 to 4 recorded at a borehole seismograph station operated by the University of Southern California at Baldwin Hills in the middle of the Newport-Inglewood fault. A procedure was developed for an accurate estimation of moment magnitude from the measurement of coda amplitude as a function of lapse time. The cumulative number of earthquakes per unit time period and area was estimated by finding the detection limit for ts-p for each magnitude. We found a clear departure of the observed log frequency-magnitude relation for M3. The observed frequency of earthquakes with M≂0.5 is almost 10 times less than that expected from the extrapolation of empirical relation for earthquakes with magnitudes larger than 3. We conclude that the observed frequency-magnitude relation departs from self-similarity for earthquakes with magnitude smaller than about 3. This departure coincides with the widely observed departure of the moment-corner frequency relation from self-similarity. These observations are consistent with the interpretation of fmax of large earthquakes in terms of the slip-weakening instability model in which the critical slip may be a few tenths of a meter to a few meters and the cohesive zone size may be a few hundred meters to a few kilometers. ¿ American Geophysical Union 1987