  We show that a new resonant magnetic excitation at incommensurate momenta,
observed recently by inelastic neutron scattering experiments on
YBa$_2$Cu$_3$O$_{6.85}$ and YBa$_2$Cu$_3$O$_{6.6}$, is a {\it spin exciton}.
Its location in the magnetic Brillouin zone and its frequency are determined by
the momentum dependence of the particle-hole continuum. We identify several
features that distinguish this novel mode from the previous resonance mode
observed near ${\bf Q}=(\pi,\pi)$, such as its intensity maximum which occurs
in a different part of the magnetic Brillouin zone.
