We present an estimation of the reionization optical depth tau from an improved analysis of data from the High Frequency Instrument (HFI) on board the Planck satellite. By using an improved version of the HFI map-making code, we greatly reduce the residual large-scale contamination a ffecting the data, characterised in, but not fully removed from, the Planck 2018 legacy release. This brings the dipole distortion systematic e ffect, contaminating the very low multipoles, below the noise level. On large-scale polarization-only data, we measure tau = 0.0566(-0).(+0)(0062).(0053) at 68% C.L., reducing the Planck 2018 legacy release uncertainty by similar to 40%. Within the Lambda CDM model, in combination with the Planck large-scale temperature likelihood, and the high-l temperature and polarization likelihood, we measure tau = 0.059 +/- 0.006 at 68% C.L., which corresponds to a mid-point reionization redshift of z(re) = 8.14 +/- 0.61 at 68% C.L. This estimation of the reionization optical depth with 10% accuracy is the strongest constraint to date.