It is shown that, when the transit electron population is taken into account, the linear stability criterion for a tearing mode of a quasineutral current sheet changes markedly, so the instability domain can exist in the WKB approximation. A new stability criterion is derived, which depends on the electron-to-ion temperature ratio. With allowance for the transit electron population, the stability of a tearing mode is shown to be also governed by the pitch-angle diffusion of electrons in a current sheet.