  RR Lyrae stars are one of the primary distance indicators for old stellar
populations such as globular clusters, dwarf galaxies and galaxies. Typically,
fundamental-mode RR Lyr stars are used for distance measurements, and their
accuracy is strongly limited by the dependence of absolute magnitudes on
metallicity, in both the optical and infrared bands. Here, we report the
discovery of a period-(period ratio)-metallicity relation for double-mode RR
Lyr stars, which can predict metallicity as accurately as the low-resolution
spectra. With theoretical and observational evidence, we propose that the
period-luminosity relation of double-mode RR Lyr stars is not affected by the
metallicity. Combining the Large Magellanic Cloud distance and Gaia parallaxes,
we calibrate the zero point of the period-luminosity relation to an error of
0.022 mag, which means that in the best case double-mode RR Lyr stars can
anchor galaxy distances to an accuracy of 1.0%. For four globular clusters and
two dwarf galaxies, we obtain distances using double-mode RR Lyr stars with a
distance accuracy of 2-3% and 1-2%, respectively. With future telescopes such
as the China Space Station Telescope and the Vera C. Rubin Observatory,
double-mode RR Lyr stars will be established as an independent distance ladder
in the near-field universe.
