  The tunneling of a giant spin at excited levels is studied theoretically in
mesoscopic magnets with a magnetic field at an arbitrary angle in the easy
plane. Different structures of the tunneling barriers can be generated by the
magnetocrystalline anisotropy, the magnitude and the orientation of the field.
By calculating the nonvacuum instanton solution explicitly, we obtain the
tunnel splittings and the tunneling rates for different angle ranges of the
external magnetic field ($\theta_{H}=\pi/2$ and $\pi/2<\theta_{H}<\pi$). The
temperature dependences of the decay rates are clearly shown for each case. It
is found that the tunneling rate and the crossover temperature depend on the
orientation of the external magnetic field. This feature can be tested with the
use of existing experimental techniques.
