The relationship between flares and coronal mass ejections (CMEs) remains a topic of active research. This paper considers a complete set of 311 M- and X-class GOES soft X-ray flares observed during the years 1996-1999. The durations of these flares have been determined as part of this study. Possible CME candidates for the 229 flares with good LASCO data coverage were identified using existing on-line catalogs. Approximately 40% of the M-class flares do not have CMEs. The probability of finding a CME candidate does not depend on the solar location of the flare, which supports the conclusion that the lack of observed CMEs is not an observational selection effect. Thresholds of 6.0×10-5Wm-2 in peak flux, 0.07 Jm-2 in total flux, and 4 hours in duration independently allow a 95% confidence in predicting that a CME will be observed. For flares with peak flux and duration below these thresholds, the fraction of flares with CME candidates is independent of the observed value of peak flux or duration. The close association between long-duration flares and CMEs reported in previous studies is not confirmed. There is the suggestion of a trend between total flux and the fraction of flares that have CME associations. The variation of the X-ray flux and flare activity over the rising phase of solar cycle 23 is considered in an appendix.