The lower hybrid drift instability is investigated in nonantiparallel reversed field plasmas, i.e., the magnetic fields on either side of a neutral line are not antiparallel. Such a magnetic field configuration contains magnetic shear, which has a stabilizing influence on the lower hybrid drift instability. It is found that magnetic shear has an inhibiting effect on the linear penetration of the lower hybrid drift mode toward the neutral line. The implications of this result to reconnection processes in the magnetosphere (i.e., the nose and the magnetotail) are discussed.