We study two rare decays, Z → π + π − and K + K − , in the perturbative QCD approach up to the nextto-leading order of the strong coupling and the leading power of 1/m Z , m Z being the Z boson mass.The branching ratios B(Z → π + π − ) = (0.83 ± 0.02 ± 0.02 ± 0.04) × 10 −12 and B(Z → K + K − ) = (1.74 +0.03 −0.05 ± 0.04 ± 0.02) × 10 −12 are obtained and can be measured at a tera-Z factory. Because the subleading-power contributions to the branching ratios are negligible, and the leading one does not depend on any free parameter, the two channels can serve as a touchstone for the applicability of the perturbative QCD approach.