  In recent years post-Newtonian approximations for isolated slowly-moving
systems in general relativity have been studied by means of matched asymptotic
expansions. A paper by Poujade & Blanchet in 2002 made great progress by
effectively reducing the use of such expansions to an algorithmic form. It gave
systematic procedures for the development of both near-zone and far-zone
asymptotic expansions, avoiding the divergent integrals which often bedevilled
such methods, and showed that these two expansions could be made to match
exactly, a result described there as somewhat remarkable.
  This paper revisits that work and shows that there is unfortunately an error
in it which invalidates the results of the matching process as given therein.
The present paper identifies that error and shows how it may be corrected to
give valid matching results. The correction is presented in a redevelopment
somewhat different from that of their paper. This shows that far from being
somewhat remarkable, it is in fact inevitable that the match is exact. It is
indeed remarkable that they could carry both expansions to the point at which
matching becomes possible, but if it can be done at all, then the match is
necessarily exact.
  A companion paper will apply this asymptotic matching to a model problem in
which the correct near-zone expansion was obtained by approximation from an
exact solution. It will be shown that there is a discrepancy between this
expansion and results from the original development of Poujade & Blanchet but
that the corrected development presented here reproduces the result of the
model problem exactly.
