We investigate the distinct properties of two types of flares: eruptive flares associated with CMEs and confined flares without CMEs. Our sample of study includes nine M and X-class flares, all from the same active region (AR), six of which are confined and three others are eruptive. The confined flares tend to be more impulsive in the soft X-ray time profiles and show more slender shapes in the EIT 195 A images, while the eruptive ones are of long-duration events and show much more extended brightening regions. The location of the confined flares are closer to the center of the AR, while the eruptive flares are at the outskirts. This difference is quantified by the displacement parameter, the distance between the AR center and the flare location: the average displacement of the six confined flares is 16 Mm, while that of eruptive ones is as large as 39 Mm. Further, through nonlinear force-free field extrapolation, we find that the decay index of the transverse magnetic field in the low corona (~10 Mm) have a larger value for eruptive flares than that for confined one. In addition, the strength of the transverse magnetic field over the eruptive flare sites is weaker than that over the confined ones. These results demonstrate that the strength and the decay index of background magnetic field may determine whether or not a flare be eruptive or confined. The implication of these results on CME models is discussed in the context of torus instability of flux rope. ; Comment: 23 pages, 8 figures, 2 tables, ApJ in press