  It is shown that the two-level correlation function $R(s,s')$ in the
invariant random matrix ensembles (RME) with soft confinement exhibits a "ghost
peak" at $s\approx -s'$. This lifts the sum rule prohibition for the level
number variance to have a Poisson-like term ${\rm var}(n)=\eta n$ that is
typical of RME with broken U(N) symmetry. Thus we conclude that the U(N)
invariance is broken spontaneously in the RME with soft confinement, $\eta$
playing the role of an order-parameter.
