In a self-consistent multicomponent envelope function approach, we showed that&khgr;xxx(2)component of the second-harmonic susceptibility tensor of a symmetricp-type quantum well (QW) exists, because of the valence-band mixing at nonzero values of the in-plane wave vector. For a highly doped narrowGaAs/Al0.3Ga0.7AsQW, our calculation indicates that at low temperatures a large value(∼10−7m/V) of&khgr;xxx(2)can be achieved in the far-infrared frequency range without satisfying double resonance conditions. This value is comparable to the experimentally observed value of&khgr;zzz(2)inn-type asymmetric QW structures. ©1997 American Institute of Physics.