  We use a new technique to extract the spectrum of a supernova from that of
the contaminating background of its host galaxy, and apply it to the specific
case of high-redshift Type Ia supernova (SN Ia) spectroscopy. The algorithm is
based on a two-channel iterative technique employing the Richardson-Lucy
restoration method and is implemented in the IRAF code 'specinholucy'. We run
the code both on simulated (SN Ia at z=0.5 embedded in a bright host galaxy)
and observed (SNe Ia at various phases up to z=0.236) data taken with VLT+FORS1
and show the advantages of using such a deconvolution technique in comparison
with less elaborate methods. This paper is motivated by the need for optimal
supernova spectroscopic data reduction in order to make meaningful comparisons
between the low and high-redshift SN Ia samples. This may reveal subtle
evolutionary and systematic effects that could depend on redshift and bias the
cosmological results derived from comparisons of local and high-z SNe Ia in
recent years. We describe the various aspects of the extraction in some detail
as guidelines for the first-time user and present an optimal observing strategy
for successful implementation of this method in future high-z SN Ia
spectroscopic follow-up programmes.
