  A new method is presented for obtaining all-electron results from a
pseudopotential calculation. This is achieved by carrying out a localised
calculation in the region of an atomic nucleus using the embedding potential
method of Inglesfield [J.Phys. C {\bf 14}, 3795 (1981)]. In this method the
core region is \emph{reconstructed}, and none of the simplifying approximations
(such as spherical symmetry of the charge density/potential or frozen core
electrons) that previous solutions to this problem have required are made. The
embedding method requires an accurate real space Green function, and an
analysis of the errors introduced in constructing this from a set of numerical
eigenstates is given. Results are presented for an all-electron reconstruction
of bulk aluminium, for both the charge density and the density of states.
