Abstract. Let F be a non-archimedean local field of residual characteristic different from 2. This paper is a first step in the description of the smooth representation theory of a unitary group G ⊂ GL(N,F) via types. We intersect certain double cosets in GL(N,F) with G and hence obtain the intertwining of certain characters ψ_β^- of open compact subgroups of G, for β ∈ Lie G. In the case when β is elliptic regular "modulo &weierp_F", we will then obtain supercuspidal representations of G.