  We present a new piece of evidence in favour of the importance of the quark
off-shellness in the kaon. The matrix elements of the flavour-changing
operators for $K_{L}\to\gamma\gamma$ comply with the general behaviour of the
matrix elements expected in the pairing bound-state model used here. The
present calculation in essence agrees with previous chiral-quark results. The
off-shell contribution turns out to be dominant (the model on-shell amplitude
being at the 10% level). Compared with the chiral perturbation-theory approach,
our off-shell contribution is an entirely new ${\cal{O}}(p^{4})$ {\em
direct-decay} piece, whereas the non-diagonal magnetic-moment term belongs to
the order ${\cal{O}}(p^{6})$.
