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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 m_b to M_s (in the range of 3.3 ≦ m_b ≦ 5.7). For this conversion, we use regression of M_s on m_b for Mexican and Central American events as well as an M_s - m_b regression based on worldwide data (Wyss and Habermann, 1982). We also take into account the standard error in M_s; this may be important since the number of events decreases as m_b increases. The M_s data of 18.5 yr is normalized to 75.5 yr and is compared to the statistics of observed large earthquakes (M_s ≧ 6.4) for the period 1906 to 1981. It is found that the G-R relation in …