In this work, we present a new, previously unknown type of structure transformation in the high-pressure gas hydrates, which is related to the existence of two different isostructural phases of the sulfur hexafluoride clathrate hydrates. Each of these phases has its own stability field on the phase diagram. The difference between these hydrates consists of partial filling of small D cages by SF6 molecules in the high-pressure phase; at 900 MPa, about half of small cages are occupied. Our calculations indicate that the increase of population of small cavities is improbable, therefore, at any pressure value, a part of the cavities remains vacant and the packing density is relatively low. This fact allowed us to suppose the existence of the upper pressure limit of hydrate formation in this system; the experimental results obtained confirm this assumption.