  The high energy spin excitation in the high T$_{c}$ cuprates is studied in
the single mode approximation for the $t-t'-J$ model. An exact form for the
mode dispersion is derived. When the Gutzwiller projected BCS state is used as
the variational ground state, a spin-wave-like dispersion of about 2.2$J$ is
uncovered along the $\Gamma=(0,0)$ to $\mathrm{M}=(\pi,0)$ line. Both the mode
energy and the integrated intensity of the spin fluctuation spectrum are found
to be almost doping independent in large doping range, which agrees very well
with the observations of recent RIXS measurements. Together with previous
studies on the quasiparticle properties of the Gutzwiiler projected BCS state,
our results indicate that such a Fermionic RVB theory can provide a consistent
description of both the itinerant and the local aspect of electronic
excitations in the high T$_{c}$ cuprates.
