A record-breaking earthquake has a larger magnitude than any previous earthquake in the study region; a starting date and minimum magnitude must be specified. The first earthquake to satisfy this condition is, by definition, a record-breaking earthquake. The next record-breaking earthquake has a larger magnitude than the first and so forth. In this article we utilize the global Centroid Moment Tensor Project (CMT) catalog for the years 1977 to 2006. We consider earthquakes with moment magnitudes greater than 5.5. We determine the number of record-breaking earthquakes nrb during 15 specified two-year intervals. We then average the nrb at specified subintervals of time. We compare the results with the predictions for a random independent and identically distributed (i.i.d.) process. The expected number of record-breaking earthquakes nrb in a specified period is independent of the statistical distribution of magnitudes. Good statistical agreement between the observations and the predictions is obtained. We carry out the same process for the magnitudes of the record-breaking earthquakes. We again compare the results with the predictions for a random (i.i.d.) process and find good agreement. For our analyses to be valid, it is necessary that the global earthquakes occur randomly, that is, they are not correlated. Thus, aftershocks and foreshocks will be sources of error. Studies of record-breaking temperatures have shown a sensitivity to global warming. A future direction for research is to apply the approach used here to regional earthquake catalogs. Aftershocks are expected to strongly influence the results.