It has been suggested previously that at the center of the earth's plasma sheet there exists a thin nonadiabatic layer, the neutral sheet, whose thickness is of the order of the ion gyroradius. The ion distribution in such a thin sheet may have some non-Maxwellian form. The purpose of this paper is to construct a one-dimensional 'non-Maxwellian' model for the steady neutral sheet and to examine its instability properties with respect to the lower-hybrid-drift (LHD) wave. A combination of a Boltzmann distribution and a modified Alpers' distribution for ions is taken. We show that in the limit of a thin neutral sheet, this distribution is a more powerful source of free energy than the usual drifting Maxwellian. It is found that most regions within the neutral sheet are unstable. The frequency spectrum of the unstable waves is nearly the same as in the drifting Maxwellian case. As shown previously by Huba et al. (1978), the frequency spectrum is in good agreement with the observations. The growth rate, assuming a modified Alpers' distribution function, is found to be enhanced compared with that due to a drifting Maxwellain model in a portion of the sheet at some distance from the null of the field. The saturation level of the fluctuating field and the anomalous resistivity are calculated in the entire sheet by using current relaxation as the stabilizing mechanism and are found to be 3--4 times larger than those in a Maxwellian sheet.