  Hierarchical mergers of galaxies can form binary black holes (BBHs) since
many or most galaxies have central massive black holes (BHs). It is possible
that some BBHs exist in active galactic nuclei (AGNs). We argue that each BH
may be surrounded by an accretion disc with a different inclination angle to
the line of sight (due to different BH spin directions and the
Bardeen-Petterson effect). The observed Fe K_alpha line profile from a BBH
system is a combination of the lines from the inner regions of the two discs,
which is significantly affected by the inclination angles of the two discs. The
Fe K_alpha line profile associated with BBHs may have an unusual shape with
double or more peaks as well as short-term variability, which can be
distinguished from the Fe K_alpha line properties of some other possible
models. We suggest that with the improvement of resolution in X-ray astronomy,
Fe K_alpha line profiles be a potential tool to probe the existence of massive
BBHs in AGNs. The Fe K_alpha line profile associated with BBHs may also provide
a tool to investigate the dynamics in strong gravitation field (e.g. providing
evidence of the Bardeen-Petterson effect).
