  Lamata et al. use an inductive approach to classify the entangled pure states
of four qubits under stochastic local operations and classical communication
(SLOCC) [PRA 75(2), 022318 (2007)]. The inductive method yields a priori ten
different entanglement superclasses, of which they discard three as empty. One
of the remaining superclasses is split in two, resulting in eight superclasses
of genuine four-qubit entanglement.
  Here, we show that two of the three discarded superclasses are in fact
non-empty and should have been retained. We give explicit expressions for the
canonical states for those superclasses, up to SLOCC and qubit permutations.
Furthermore, we confirm that the third discarded superclass is indeed empty,
yielding a total of ten superclasses of genuine four-qubit entanglement under
the inductive classification scheme.
