Dual solutions for steady natural convection of air between two horizontal concentric cylinders are numerically investigated in the range of $D_i$/L(=diameter of inner cylinder/gap width)$leq$10. It is found that, when the Rayleigh number based on the gap width exceeds a certain critical value, a new flow pattern forming two counter-rotating eddies in the half of the annulus can be realized, which is different from the crescent-shaped flow commonly observed. In the new flow pattern, the fluid near the top of the hot inner cylinder moves downward. This solution is found for D$_{i}$/L.geq.0.3, but not for$D_i$/TEX>/L$leq$0.2. As <TEX>$D_i$/TEX>/L increase, the critical Rayleigh number is decreased, and tends to a finite limit.t.