  The double-layer electron system with total filling factor $\nu=1/2$ can be
regarded as two separate Fermi-liquid-like states with $\nu=1/4$ when the layer
separation is sufficiently large and there is no tunneling. The weak tunneling
in this state suffers an orthogonality catastrophe and it becomes irrelevant.
Using the symmetric and antisymmetric combinations of layer indices as the
pseudospin degrees of freedom, we show that there exists the first order
transition from the above pseudospin unpolarized state to the pseudospin
polarized Fermi-liquid-like state with $\nu=1/2$ as the tunneling strength
becomes sufficiently large.
