This paper is for the investigation of the relationship between the geomagnetic disturbances and the relativistic electron events occurring at geosynchronous orbit. We have analyzed the electron fluxes of E > 2 MeV measured by GOES 10 satellite and the hourly Dst index for the period of April, 1999 to December, 2002. With the rigorous definition of the relativistic event, total 34 events were identified during the time period. Our statistical study showed that more than 50% of the total events occurred associated with weak (or sometimes virtually no) magnetic storms. And only ~ 20% of the events took place accompanied by a strong magnetic storm of $Dst_{min}$ < -100 nT. This result suggests that large geomagnetic storms may not be crucial for the occurrence of a relativistic event at geosynchronous orbit. We also found that there is no clear correlation between the maximum electron flux of an event and the associated minimum of Dst. Therefore any study on the physical mechanism (s) accounting for the relativistic events should take it into account that strong magnetic storms may not be necessarily required for the occurrence of a relativistic electron event at geosynchronous orbit.