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Nonlocality without entanglement is an interesting field. A manifestation ofquantum nonlocality without entanglement is the local indistinguishability of aset of orthogonal product states. In this paper we analyze the character ofoperators 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 onlylocal projective measurements and classical communication, and thesemeasurements cannot damage each product basis. Employing these conclusions onecan discuss local distinguishability of full product bases easily. Finally wediscuss the generalization of these results to the locally distinguishabilityof a set of incomplete product bases

Distinguishing the elements of a full product basis set needs only projective measurements and classical communication