  Let G be the unramified unitary group in three variables defined over a
p-adic field F of odd residual characteristic. In this paper, we investigate
local newforms for irreducible admissible representations of G. We introduce a
family of open compact subgroups {K_n} of G to define the local newforms for
representations of G as the K_n-fixed vectors. We prove the existence of local
newforms for generic representations and the multiplicity one property of the
local newforms for admissible representations.
