  We analyze a modification of the BFKL kernel for the adjoint representation
of the colour group in the maximally supersymmetric (N=4) Yang-Mills theory in
the limit of a large number of colours, related to the modification of the
eigenvalues of the kernel suggested by S. Bondarenko and A. Prygarin in order
to reach the Hermitian separability of the eigenvalues. We restore the modified
kernel in the momentum space. It turns out that the modification is related
only to the real part of the kernel and that the correction to the kernel can
not be presented by a single analytic function in the entire momentum region,
which contradicts the known properties of the kernel.
