Total column ozone (TCO) data from multiple satellite-based instruments have been combined to create a single near-global daily time series of ozone fields at 1.25degree longitude by 1degree latitude spanning the period 31 October 1978 to 31 December 2019. Comparisons against TCO measurements from the ground-based Dobson and Brewer spectrophotometer networks are used to remove offsets and drifts against the ground-based measurements in a subset of the satellite-based instruments. The corrected subset is then used as a basis for homogenizing the remaining data sets. The intention is that this data set serves as a climate data record for TCO and, to this end, the requirements for constructing climate data records, as detailed by GCOS (Global Climate Observing System) have been followed as closely as possible. The construction of this database improves on earlier versions of the database maintained first by the National Institute of Water and Atmospheric Research (NIWA) and now by Bodeker Scientific (BS). Please note: For the reasons detailed in this document, version 3.5.1 of the NIWA-BS TCO database should not be used henceforth for trend analysis and, as such, we have updated the version 3.4 database to the end of 2019 (now referred to as version 3.4.1 of the database) as a replacement. You will find a link to version 3.4.1 under the link provided above. This version 3.5.1. is produced using the same method as version 3.4 but the dataset has been extended in time to the end of 2019. This means that all fits were recalculated and, thus, this version is slightly different to version 3.4 in all years. A filled (gap-free) version of this dataset is available under https://doi.org/10.5281/zenodo.4535247. The data are available in daily, monthly or annual resolution. Please note the following for the data in monthly and annual resolution: Monthly: There have to be at least 25 valid values in a gridbox within a month to calculate a monthly mean. Annual: There have to be at least 12 valid monthly values within a year to calculate an annual mean. Please email greg@bodekerscientific.com and let us know which data set you downloaded and what your intended purpose for the use of the data is. You will then receive updates if an improved version becomes available.