  The analytic result for the radiative correction of order
$\alpha^{2}(Z\alpha)^{5}m$ to the Lamb shift connected with a polarization
insertion in one of the two external Coulomb lines is obtained. This correction
arises from a gauge invariant set of diagrams which contain, besides the
polarization insertion in the Coulomb leg, all one-loop radiative photon
insertions in the electron line with two external Coulomb lines.
