  We present a criterion of separability for arbitrary s partitions of
N-particle fermionic pure states. We show that, despite the superficial
non-factorizability due to the antisymmetry required by the
indistinguishability of the particles, the states which meet our criterion have
factorizable correlations for a class of observables which are specified
consistently with the states. The separable states and the associated class of
observables share an orthogonal structure, whose non-uniqueness is found to be
intrinsic to the multi-partite separability and leads to the non-transitivity
in the factorizability in general. Our result generalizes the previous result
obtained by Ghirardi et. al. [J. Stat. Phys. 108 (2002) 49] for the s = 2 and s
= N case.
