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Stable sheet electron-beam transport is critical for sheet-beam microwave device which is attractive for high-power millimeter wave to terahertz-regime radiation. This paper studies the stable sheet-beam transport in periodic nonsymmetric quadrupole field. First, the conditions for stable round- and sheet-beam transport in periodic magnetic quadrupole field are deduced. In the deduction, we find that the symmetric quadrupole field and the space-charge field of sheet beam are not well matched. In order to settle this problem, we use periodic nonsymmetric quadrupole field instead of periodic symmetric quadrupole field to transport sheet beam. Finally, 3-D PIC simulations verify the conditions for stable sheet-beam transport and show that periodic nonsymmetric quadrupole field is intrinsically well suited for sheet-beam transport.