  The shape and the inverse participation ratio (IPR) of local spectral density
(LSD) are studied for a generic isolated system of coupled quantum states, the
Hamiltonian of which is represented by a band random matrix with the disordered
leading diagonal. We find for the matrices with arbitrary small band that the
lack of ergodicity for LSD can be associated with an exponential increase in
IPR with the ratio $v/\Delta_c$ ($v$ - the root of mean square for off-diagonal
matrix elements, $\Delta_c$ - the energy spacing between directly coupled basis
states). Criterions specifying transition to localization and ergodicity for
LSD are considered.
