  We prove that every irreducible, admissible representation of GSp(4,F), where
F is a non-archimedean local field of characteristic zero, admits a Bessel
functional, provided the representation is not one-dimensional. Given such a
representation, we explicitly determine the set of all split Bessel functionals
admitted by the representation, and prove that these functionals are unique. If
the representation is not supercuspidal, or in an L-packet with a
non-supercuspidal representation, we explicitly determine the set of all Bessel
functionals admitted by the representation, and prove that these functionals
are unique.
