A remarkable flexibility is observed in biological membranes, which allows them to form the structures of different curvatures. We addressed the question of intrinsic ability of phospholipid membranes to form highly curved structures and the role of cholesterol in this process. The distribution of cholesterol in the highly curved asymmetric DOPC/DOPS lipid bilayer was investigated by the coarse-grained molecular dynamics simulations in the membrane patches with large aspect ratio. It is shown that cholesterol induces uneven membrane curvature promoting the formation of extended flattened regions of the membrane interleaved by sharp bends. It is shown that the affinity of cholesterol to anionic DOPS or neutral DOPC lipids is curvature dependent. The cholesterol prefers DOPS to DOPC in either planar or highly curved parts of the membrane. In contrast, in the narrow interval of moderate membrane curvatures this preference is inverted. Our data suggest that there is a complex self-consistent interplay between the membrane curvature and cholesterol distribution in the asymmetric lipid bilayers. The suggested new function of cholesterol may have a biological relevance.