  We present an expression for the operator of the electric quadrupole
hyperfine interaction which takes into account finite nuclear size. We compare
the results obtained with the use of this operator with those obtained in the
standard approach which ignores finite nuclear size. We found that the effect
of changing operators on the hyperfine constant $B$ is small in hydrogen-like
systems. There is a very significant enhancement of the effect in many-electron
atoms caused by the contribution of the large $s_{1/2}-d_{3/2},d_{5/2}$ and
$p_{1/2}-p_{3/2}$ off diagonal matrix elements to the core polarisation,
correlation and configuration interaction corrections. Similar enhancement
takes place for transition amplitudes induced by the electric quadrupole
hyperfine interaction.
