  We study the distribution of complex eigenvalues $z_1,\ldots, z_N$ of random
Hermitian $N\times N$ block band matrices with a complex deformation of a
finite rank. Assuming that the width of the band $W$ grows faster than
$\sqrt{N}$, we proved that the limiting density of $\Im z_1,\ldots, \Im z_N$ in
a sigma-model approximation coincides with that for the Gaussian Unitary
Ensemble. The method follows the techniques of arXiv:1802.03813
