  We propose an inductive procedure to classify N-partite entanglement under
stochastic local operations and classical communication (SLOCC) provided such a
classification is known for N-1 qubits. The method is based upon the analysis
of the coefficient matrix of the state in an arbitrary product basis. We
illustrate this approach in detail with the well-known bi- and tripartite
systems, obtaining as a by-product a systematic criterion to establish the
entanglement class of a given pure state without resourcing to any entanglement
measure. The general case is proved by induction, allowing us to find an upper
bound for the number of N-partite entanglement classes in terms of the number
of entanglement classes for N-1 qubits.
