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Context. RR Lyrae stars are useful standard candles allowing one to deriveaccurate distances for old star clusters. Based on the recent catalogues fromOGLE-IV and Gaia Early Data Release 3 (EDR3), the distances can be improved fora few bulge globular clusters. Aims. The aim of this work is to derive anaccurate distance for the following six moderately metal-poor, relativelyhigh-reddening bulge globular clusters: NGC 6266, NGC 6441, NGC 6626, NGC 6638,NGC 6642, and NGC 6717. Methods. We combined newly available OGLE-IV cataloguesof variable stars containing mean I magnitudes, with Clement's previouscatalogues containing mean V magnitudes, and with precise proper motions fromGaia EDR3. Astrometric membership probabilities were computed for each RRLyrae, in order to select those compatible with the cluster proper motions.Applying luminosity-metallicity relations derived from BaSTI $\alpha$-enhancedmodels (He-enhanced for NGC 6441 and canonical He for the other clusters), weupdated the distances with relatively low uncertainties. Results. Distanceswere derived with the I and V bands, with a $5-8\%$ precision. We obtained 6.6kpc, 13.1 kpc, 5.6 kpc, 9.6 kpc, 8.2 kpc, and 7.3 kpc for NGC 6266, NGC 6441,NGC 6626, NGC 6638, NGC 6642, and NGC 6717, respectively. The results are inexcellent agreement with the literature for all sample clusters, consideringthe uncertainties. Conclusions. The present method of distance derivation,based on recent data of member RR Lyrae stars, updated BaSTI models, and robuststatistical methods, proved to be consistent. A larger sample of clusters willbe investigated in a future work.

Precise distances from OGLE-IV member RR Lyrae stars in six bulge globular clusters