  A much improved determination of the transverse energy of jets has been
carried out in ZEUS, using a correction procedure based on two independent
methods. The first is based on a combination of tracking and calorimeter
information which optimises the resolution of reconstructed kinematic
variables. The conservation of energy and momentum in neutral current deep
inelastic e^+p scattering events is exploited to determine the energy
corrections by balancing the kinematic quantities of the scattered positron
with those of the hadronic final state. The method has been independently
applied to data and simulated events. The second method uses calorimeter cells
as inputs to the jet algorithm. Simulated events are then used to provide a
correction for the energy loss due to inactive material in front of the
calorimeter. A detailed comparison of the jet transverse energy and the
transverse energy of tracks in a cone around the jet provides the final
correction. This procedure relies on an accurate simulation of charged tracks
and so is less reliant on simulating the energy loss of neutral particles in
inactive material. Final comparisons of the data and simulated events for both
methods allow an uncertainty +/- 1% to be assigned to the jet energy scale.
