Vela X is a region of extended radio emission in the western part of the Vela constellation: one of the nearest pulsar wind nebulae, and associated with the energetic Vela pulsar. A deeper observation of the entire Vela X nebula region, also including larger offsets from the cocoon, has been performed with HESS. This re-observation was carried out in order to probe the extent of the non-thermal emission from the Vela X region at TeV energies and to investigate its spectral properties. To increase the sensitivity to the faint gamma -ray emission from the very extended Vela X region, a multivariate analysis method combining three complementary reconstruction techniques of Cherenkov-shower images is applied for the selection of gamma -ray events. The Vela X region exhibits almost uniform gamma -ray spectra over its full extent: the differential energy spectrum can be described by a power-law function with a hard spectral index ... and an exponential cutoff at an energy of TeV.(ProQuest: ... denotes formulae/symbols omitted.)