  The broad X-ray iron line, detected in many active galactic nuclei, is likely
to be produced by fluorescence from the X-ray illuminated central parts of an
accretion disc close to a supermassive black hole. The time-averaged shape of
the line can be explained most naturally by a combination of special and
general relativistic effects. Such line profiles contain information about the
black hole spin and the accretion disc as well as the geometry of the emitting
region and may help to test general relativity in the strong gravity regime. In
this paper we embark on the computation of the temporal response of the line to
the illuminating flux. Previous studies concentrated on the calculation of
reverberation signatures from static sources illuminating the disc. In this
paper we focus on the more physically justified case of flares located above
the accretion disc and corotating with it. We compute the time dependent iron
line taking into account all general relativistic effects and show that its
shape is of very complex nature, and also present light curves accompanying the
iron line variability. We suggest that future X-ray satellites like XMM or
Constellation-X may be capable of detecting features present in the computed
reverberation maps.
