The present work investigates effects of the corner recirculation zone (CRZ) on flame macrostructures and combustion instabilities in the Beihang Axial Swirler Independently Stratified (BASIS) burner, a double-swirled full-scale burner characterized by separated stratified swirling flames at atmospheric pressure supplied with methane/air mixture. Three different macrostructures are observed, i.e. a lifted L-flame, a double-conical S-flame and a single conical V-flame as the stratification ratio (SR, the ratio of the inner stream equivalence ratio to the outer stream equivalence ratio) varies from 0.25 to 2.50 at a fixed total equivalence ratio of 0.6. It is found that the penetration of the flame into the corner recirculation zone leads to a sudden increase of acoustic oscillation. Rayleigh index maps confirm the driving effect of the CRZ region on combustion instabilities for the 0.25 ≤ SR ≤ 1.75 cases. When the corner recirculation zone is removed by the use of segmented confinements, similar flame macrostructures arise in the same SR range. More interestingly, the combustion instability is suppressed under all stratification ratios. A parametric experiment is also performed to confirm the generality of above findings, including three types of the segmented confinement, two premixednesses of the outer flame and a wider range of operating conditions. The suppressive effect is outstanding in all segmented confinements. The present study reveals the effect of the corner recirculation zone on combustion instabilities and demonstrates a potential method for passive control.