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Let F_0 be a non-archimedean local field of odd residual characteristic andlet G be the non quasi-split unramified unitary group in four variables definedover F_0. In this paper, we give a classification of the irreducible smoothrepresentations of G of non-integral level using the Hecke algebraic methoddeveloped by Howe and Moy.

Representations of non quasi-split unramified U(4) over a p-adic field I:Representations of non-integral level