  In [M. Walter et al., Science 340, 1205, 7 June (2013)], via polytopes they
gave a sufficient condition for genuinely entangled pure states and discussed
SLOCC classification. In this paper, we study entanglement classification of
pure states of $n$ qubits via the basis state matrix (BSM) whose rows are the
basis states. We propose a canonical form of BSM obtained by exchanging columns
(i.e. permutation of qubits) and rows of BSM and then a necessary and
sufficient condition for a genuinely entangled state of n qubits via a
canonical form of BSM. Thus, for any $n$ qubits, the genuinely entangled states
can be partitioned into two families. One family includes all states whose BSM
cannot be transformed into the canonical form. The states with the BSM are
always genuinely entangled no matter what the non-zero coefficients are. GHZ
and W states belong to the family. The other includes all states whose BSM can
be transformed into the canonical form, but for any canonical form of BSM, some
two columns or rows of the corresponding coefficient matrix are not
proportional. The cluster state belongs to the family.
