Nonlocality without entanglement is an interesting field. A manifestation of
quantum nonlocality without entanglement is the local indistinguishability of a
set of orthogonal product states. In this paper we analyze the character of
operators to distinguish a set of full product bases in a multi-partite system,
and show that distinguishing perfectly a set of full product bases needs only
local projective measurements and classical communication, and these
measurements cannot damage each product basis. Employing these conclusions one
can discuss local distinguishability of full product bases easily. Finally we
discuss the generalization of these results to the locally distinguishability
of a set of incomplete product bases