A linear local kinetic analysis of a modified lower hybrid drift (LHD) instability near the neutral plane of a current sheet with a normal component of the magnetic field Bz is carried out. It is shown that in nearly drift-free configurations the stabilizing effects of high plasma beta (cross-field wave-particle resonance) are significantly reduced in comparison with straight or current-free magnetic field geometries. A parameter &agr;0 characterizing the degree of local deviation of the system from the drift-free configuration is introduced. The sign of this parameter characterizes the direction of the bounce averaged electron drift and depends on the value of the local gradient of the normal component of the magnetic field. It is shown that a modified LHD mode can be excited if this parameter exceeds a critical value &agr;cr. For quiet time magnetostatic models of the magnetotail the parameter &agr;0 is below but very close to the critical value. It is suggested that in the course of magnetospheric convection the threshold condition for instability development could be locally satisfied which should result in generation of low-frequency magnetic noise burst (f<1 Hz) at the neutral sheet.