  We investigate the double-layer electron system in a parabolic quantum well
at filling factor $\nu=2$ in a tilted magnetic field using capacitance
spectroscopy. The competition between two ground states is found at the Zeeman
splitting appreciably smaller than the symmetric-antisymmetric splitting.
Although at the transition point the system breaks up into domains of the two
competing states, the activation energy turns out to be finite, signaling the
occurrence of a new insulator-insulator quantum phase transition. We interpret
the obtained results in terms of a predicted canted antiferromagnetic phase.
