The validity of the Gutenberg-Richter (G-R) frequency-magnitude relation over a wide range of magnitudes is usually accepted, and the statistics of small earthquakes is often extrapolated to predict the frequency of occurrence of large earthquakes. We take NOAA and PDE data from 1963 to 1981 related to the Mexican subduction zone (H ≦ 65 km) and convert mb to Ms (in the range of 3.3 ≦ mb ≦ 5.7). For this conversion, we use regression of Ms on mb for Mexican and Central American events as well as an Ms - mb regression based on worldwide data (Wyss and Habermann, 1982). We also take into account the standard error in Ms; this may be important since the number of events decreases as mb increases. The Ms data of 18.5 yr is normalized to 75.5 yr and is compared to the statistics of observed large earthquakes (Ms ≧ 6.4) for the period 1906 to 1981. It is found that the G-R relation in the range 4.5 ≲ Ms ≲ 6.0, when extrapolated, grossly underestimates the observed frequency of large earthquakes (Ms ≧ 6.5) for the Oaxaca and Jalisco regions. There is strong evidence that the plate interface in the Oaxaca region consists of a few (3 or 4) large fault zones each of which cyclically ruptures over its entire dimension without giving rise to smaller events in the manner implied by the G-R relation. The result is of profound importance in seismic risk analysis and in the understanding of fault mechanics. This phenomenon has been reported for only a few regions (e.g., Turkey: Båth, 1981; Japan: Wesnousky et al., 1983); it may have escaped detection in other regions due to a variety of causes, the most important being the long recurrence periods of large earthquakes.