  Details of the calculation of the non-forward BFKL kernel at next-to-leading
order (NLO) are offered. Specifically we show the calculation of the two-gluon
production contribution. This contribution was the last missing part of the
kernel. Together with the NLO gluon Regge trajectory, the NLO contribution of
one-gluon production and the contribution of quark-antiquark production which
were found before it defines the kernel completely for any colour state in the
$t$-channel, in particular the Pomeron kernel presented recently.
