We have examined the relationship between the speeds of coronal mass ejections (CMEs) and the GOES X-ray peak fluxes of associated flares. Noting that previous studies were possibly affected by projection effects and random association effects, we have considered two sets of carefully selected CME-flare events: four homologous events and four well-observed limb events. In the respective samples, good correlations are found between the CME speeds and the GOES X-ray peak fluxes of the associated flares. A similarly good correlation is found for all eight events of both samples when the CME speeds of the homologous events are corrected for projection effect. Our results suggest that a close relationship possibly exists between CME kinematics and flaring processes.