Abstract: A new generalized energy is propo sed to act as Ly apuno vfunction and thus a new criterion of nonlinear bar ot ropic stability containing two inequalities is obtained.One of the inequalities is that the initial disturbance amplitude is less than a critical value,and the other is that the frictional coefficient is more than another critical value.The former adds a strong rest riction to the latter,a usual nonlinear stability criterion,thus denoting that the subcritical inst ability easily occurs for a finite-amplitude disturbance in the realatm osphere.The new criterion has great himproved the previous results.