  The magnetic spectrum at high-energies in heavily underdoped
YBa$_{2}$Cu$_{3}$O$_{6.35}$ (T$_{c}$=18 K) has been determined throughout the
Brillouin zone. At low-energy the scattering forms a cone of spin excitations
emanating from the antiferromagnetic (0.5, 0.5) wave vector with an acoustic
velocity similar to that of insulating cuprates. At high energy transfers,
below the maximum energy of 270 meV at (0.5, 0), we observe zone boundary
dispersion much larger and spectral weight loss more extensive than in
insulating antiferromagnets. Moreover we report phenomena not found in
insulators, an overall lowering of the zone-boundary energies and a large
damping of $\sim$ 100 meV of the spin excitations at high-energies. The energy
above which the damping occurs coincides approximately with the gap determined
from transport measurements. We propose that as the energy is raised the spin
excitations encounter an extra channel of decay into particle-hole pairs of a
continuum that we associate with the pseudogap.
