  In his 1953 paper [Matem.~Sbornik \textbf{33} (1953), 597 -- 626] Mark Krein
presented an example of a symmetric rank one perturbation of a self-adjoint
operator such that for all values of the spectral parameter in the interior of
the spectrum, the difference of the corresponding spectral projections is not
trace class. In the present note it is shown that in the case in question this
difference has simple Lebesgue spectrum filling in the interval $[-1,1]$ and,
therefore, the pair of the spectral projections is generic in the sense of
Halmos but not Fredholm.
