  In this paper a new method is presented to find the transfer function of the
broad-line region in active galactic nuclei. The subtractive optimally
localized averages (SOLA) method is a modified version of the Backus-Gilbert
method and is presented as an alternative to the more often used
maximum-entropy method. The SOLA method has been developed for use in
helioseismology. It has been applied to the solar oscillation frequency
splitting data currently available to deduce the internal rotation rate of the
sun. The original SOLA method is reformulated in the present paper to cope with
the slightly different problem of inverting time series. We use simulations to
test the viability of the method and apply the SOLA method to the real data of
the Seyfert-1 galaxy NGC 5548. We investigate the effects of measurement errors
and how the resolution of the TF critically depends upon both the sampling rate
and the photometric accuracy of the data. A uuencoded compressed postscript
file of the paper which includes the figures is available by anonymous ftp at
ftp://solaris.astro.uu.se/pub/articles/atmos/frank/PijWan.uue
