  The determination of the primary energy of extensive air showers using the
fluorescence detection technique requires an estimation of the energy carried
away by particles that do not deposit all their energy in the atmosphere. This
estimation is typically made using Monte Carlo simulations and thus depends on
the assumed primary particle mass and on model predictions for neutrino and
muon production. In this work we present a new method to obtain the invisible
energy from events detected by the Pierre Auger Observatory. The method uses
measurements of the muon number at ground level, and it allows us to reduce
significantly the systematic uncertainties related to the mass composition and
the high energy hadronic interaction models, and consequently to improve the
estimation of the energy scale of the Observatory.
