In order to improve the success rate of auto-reclosing on the double circuit ultra-high voltage（UHV） transmission lines， the secondary arc must be restricted to a low level. In light of the neutral reactor widely used in UHV transmission lines， the mechanism of secondary arc generation is studied and the transposition effect on the restriction of secondary arc current is discussed. And the formula is given that directly calculates the impedance of the neutral reactor. Results obtained show that， in consideration of the restriction on secondary arc and the difficulty in its implementation， the reverse phase sequence transposition is best. The example shows that the formula proposed is feasible and accurate in rapidly computing the neutral reactor of double circuit transmission lines.