  Let $\rk$ be a local field of characteristic zero. Let $\pi$ be an
irreducible admissible smooth representation of $\GL_{2n}(\rk)$. We prove that
for all but countably many characters $\chi$ of $\GL_n(\rk)\times \GL_n(\rk)$,
the space of $\chi$-equivariant (continuous in the archimedean case) linear
functionals on $\pi$ is at most one dimensional. Using this, we prove the
uniqueness of twisted Shalika models.
