In a recent study Andrews found that approximately 40% of M-class flares between 1996 and 1999, classified according to GOES X-ray flux, are not associated with Coronal Mass Ejections (CMEs). Using 133 events from his dataset for which suitable photospheric magnetograms and coronal images were available, we studied the pre-flare coronal helicity of the active regions that produced big flares. The coronal magnetic field of 78 active regions was modeled under the “constant $\alpha$” linear force-free field assumption. We find that in a statistical sense the pre-flare value of $\alpha$ and coronal helicity of the active regions producing big flares that do not have associated CMEs is smaller than the coronal helicity of those producing CME-associated big flares. A further argument supporting this conclusion is that for the active regions whose coronal magnetic field deviates from the force-free model, the change of the coronal sign of $\alpha$ within an active region is twice more likely to occur when the active region is about to produce a confined flare than a CME-associated flare. Our study indicates that the amount of the stored pre-flare coronal helicity may determine whether a big flare will be eruptive or confined.To search for other articles by the author(s) go to: http://adsabs.harvard.edu/abstract_service.html