  Context. Elemental abundances in some coronal structures differ significantly
from photospheric abundances, with a dependence on the first ionization
potential (FIP) of the element. Measuring these FIP-dependent abundance biases
is important for coronal and heliospheric physics.
  Aims. We aim to build a method for optimal determination of FIP biases in the
corona from spectroscopic observations in a way that is in practice independent
from Differential Emission Measure (DEM) inversions.
  Methods. We optimised linear combinations of spectroscopic lines of low-FIP
and high-FIP elements so that the ratio of the corresponding radiances yields
the relative FIP bias with good accuracy for any DEM in a small set of typical
DEMs.
  Results. These optimised linear combinations of lines allow retrieval of a
test FIP bias map with good accuracy for all DEMs in the map. The results also
compare well with a FIP bias map obtained from observations using a
DEM-dependent method.
  Conclusions. The method provides a convenient, fast, and accurate way of
computing relative FIP bias maps. It can be used to optimise the use of
existing observations and the design of new observations and instruments.
