It is fairly easy to see from the formalism of the L group that the L group of a quasisplit unitary group will be a nontrivial semidirect product of $GL_n(\mathbb{C})$ (for the appropriate value of $n$), and a group of order two. When $n$ is odd this determines the isomorphism class uniquely. When $n$ is even, it does not. Indeed, an outer automorphism is of the form $g \mapsto A{}^tg^{-1}A^{-1}$ for some $A \in GL_n(\mathbb C).$ It is of order two if and only if $A$ is either symmetric or skew-symmetric. It seems to me that in the literature the $L$ group of a quasisplit unitary group is consistently defined using a skew-symmetric $A.$ Can anyone explain why this is correct?