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We study the condensation of localized tachyon in non-supersymmetric orbifold${\C^2/\Z_n}$. We first show that the G-parities of chiral primaries arepreserved under the condensation of localized tachyon(CLT) given by the chiralprimaries. Using this, we finalize the proof of the conjecture that thelowest-tachyon-mass-squared increases under CLT at the level of type II stringwith full consideration of GSO projection. We also show the equivalence betweenthe $G$-parity given by $G=[jk_1/n]+ [jk_2/n]$ coming from partition functionand that given by $G=\{jk_1/n\}k_2 -\{jk_2/n\}k_1$ coming from the monomialconstruction for the chiral primaires in the dual mirror picture.Comment: 12 pages, 2 figures, final form to appear in JHE

Localized tachyon condensation and G-parity conservation