  In this paper, we study the l-adic cohomology of the Rapoport-Zink tower for
GSp(4). We prove that the smooth representation of GSp_4(Q_p) obtained as the
i-th compactly supported l-adic cohomology of the Rapoport-Zink tower has no
quasi-cuspidal subquotient unless i=2,3,4. Our proof is purely local and does
not require global automorphic methods.
