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Boron, a nearest-neighbor of carbon, is possibly the second element that can possess free-standing flat monolayer structures, evidenced by recent successful synthesis of single-walled and multiwalled boron nanotubes (MWBNTs). From an extensive structural search using the first-principles particle-swarm optimization (PSO) global algorithm, two boron monolayers (α(1)- and β(1)-sheet) are predicted to be the most stable α- and β-types of boron sheets, respectively. Both boron sheets possess greater cohesive energies than the state-of-the-art two-dimensional boron structures (by more than 60 meV/atom based on density functional theory calculation using PBE0 hybrid functional), that is, the α-sheet previously predicted by Tang and Ismail-Beigi and the g(1/8)- and g(2/15)-sheets (both belonging to the β-type) recently reported by Yakobson and co-workers. Moreover, the PBE0 calculation predicts that the α-sheet is a semiconductor, while the α(1)-, β(1)-, g(1/8)-, and g(2/15)-sheets are all metals. When two α(1) monolayers are stacked on top each other, the bilayer α(1)-sheet remains flat with an optimal interlayer distance of ~3.62 Å, which is close to the measured interlayer distance (~3.2 Å) in MWBNTs.