  We find that the structure constants 4-form of a metric 3-Lie algebra is the
sum of the volume forms of orthogonal 4-planes proving a conjecture in
math/0211170. In particular, there is no metric 3-Lie algebra associated to a
$\mathfrak{u}(N)$ Lie algebra for $N>2$. We examine the implication of this
result on the existence of a multiple M2-brane theory based on metric 3-Lie
algebras.
