Using the results of Sundman and Birkhoff, as well as the previous own studies on the generalized Hill’s curves, the authors give a new method for computing a lower bound of the moment of inertia for the bounded orbits in the general three-body problem. This study gives a better lower bound of the minimum of the moment of inertia for the bounded orbits, than in the classical results, which can be used as a criterion of escape in numerical experiments. When the integral of energy goes to zero, the lower bound goes to the minimum moment of inertia of the corresponding parabolic Euler motion with the same angular momentum, which is then the greatest lower bound. The orbit of the smallest mass is the most instable one.