The present article discusses the stability of the thin current sheet against lower‐hybrid‐drift (LHDI) and modified‐two‐stream (MTSI) instabilities. It is demonstrated that MTSI is driven by the cross‐field current, implying that MTSI should also be most effective at the neutral sheet, while LHDI is driven by the density gradient, which is maximized near the edge of the current sheet. It is shown that under a normal Harris current sheet condition, Vi/∣Ve∣ = Ti/Te, LHDI completely dominates MTSI, which implies that linearly unstable current‐driven modes cannot penetrate to the center of the Harris current sheet. However, if the Harris current sheet condition is relaxed to Vi/∣Ve∣ > Ti/Te, then MTSI is shown to gradually overtake LHDI. This finding indicates that cross‐field drift linear instability dominated by MTSI feature may be operative at the center of the ion‐dominated thin current sheet.