  Compatibility of gluon Reggeization with s-channel unitarity requires the
vertices of the Reggeon interactions to satisfy a series of bootstrap
conditions. In order to derive, in the next-to-leading order (NLO), conditions
related to the gluon production amplitudes, we calculate the s-channel
discontinuities of these amplitudes and compare them with those required by the
Reggeization. It turns out that these conditions include the so called strong
bootstrap conditions for the kernel and for the impact factors of scattering
particles, which were proposed earlier without derivation, and recently were
proved to be satisfied. Besides this, there is a new bootstrap condition, which
relates a number of Reggeon vertices and the gluon trajectory.
