  We consider QM with non-Hermitian quasi-diagonalizable Hamiltonians, i.e. the
Hamiltonians having a number of Jordan cells in particular biorthogonal bases.
The "self-orthogonality" phenomenon is clarified in terms of a correct spectral
decomposition and it is shown that "self-orthogonal" states never jeopardize
resolution of identity and thereby quantum averages of observables. The example
of a complex potential leading to one Jordan cell in the Hamiltonian is
constructed and its origin from level coalescence is elucidated. Some puzzles
with zero-binorm bound states in continuous spectrum are unraveled with the
help of a correct resolution of identity.
