  It was recently conjectured by Shabad and Usov that there exists in QED a
maximum magnetic field of 10^{42} G, above which the magnetized vacuum becomes
unstable. Using a nonperturbative analysis that consistently incorporates the
effective electron mass and the screening effect in a strong magnetic field, we
show that the conjectured phenomenon of positronium collapse never takes place.
Thus, there does not exist a maximum magnetic field in QED and the magnetized
vacuum is stable for all values of the magnetic field.
