  How does one compute the Bondi mass on an arbitrary cut of null infinity
$\scri$ when it is not presented in a Bondi system? What then is the correct
definition of the mass aspect? How does one normalise an asymptotic translation
computed on a cut which is not equipped with the unit-sphere metric? These are
questions which need to be answered if one wants to calculate the Bondi-Sachs
energy-momentum for a space-time which has been determined numerically. Under
such conditions there is not much control over the presentation of $\scri$ so
that most of the available formulations of the Bondi energy-momentum simply do
not apply. The purpose of this article is to provide the necessary background
for a manifestly conformally invariant and gauge independent formulation of the
Bondi energy-momentum. To this end we introduce a conformally invariant version
of the GHP formalism to rephrase all the well-known formulae. This leads us to
natural definitions for the space of asymptotic translations with its
Lorentzian metric, for the Bondi news and the mass-aspect. A major role in
these developments is played by the "co-curvature", a naturally appearing
quantity closely related to the Gau{\ss} curvature on a cut of~$\scri$.
