  We introduce a broad lemma, one consequence of which is the higher order
singular value decomposition (HOSVD) of tensors defined by DeLathauwer, DeMoor
and Vandewalle (2000). By an analogous application of the lemma, we find a
complex orthogonal version of the HOSVD. Kraus' (2010) algorithm used the HOSVD
to compute normal forms of almost all $n$-qubit pure states under the action of
the local unitary group. Taking advantage of the double cover
$\operatorname{SL}_2(\mathbb{C}) \times \operatorname{SL}_2(\mathbb{C}) \to
\operatorname{SO}_4({\mathbb{C}})$, we produce similar algorithms
(distinguished by the parity of $n$) that compute normal forms for almost all
$n$-qubit pure states under the action of the SLOCC group.
