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Spin-dependent transmission coefficients as a function of Fermi energy is calculated for electron scattering from magnetic impurity in a narrow quantum wire, in which spin-exchange interaction between conducting electron and the impurity leads to exchange spin-flip scattering. Transmission in the spin-flipped channels is explicitly calculated. It has been found that spin-up and spin-down transmission coefficients for intrasubband and intersubband enhance Fano-resonance profiles, which have asymmetric behaviors, whenever Fermi energy crosses bottom of every subband below. Meanwhile due to dephasing of electron wave caused by spin-flip scattering,the entanglement between spin states of electron and magnetic impurity obviously destroys the global step structure of quantized conductance and suppresses the height of the conductance step.