Because of changes in SST sampling methods in the 1940s and earlier, there are biases in the earlier period SSTs relative to the most recent fifty years. Published results from the UK Met Office have shown the need for historic bias correction and developed several correction techniques. An independent bias-correction method is developed here from an analysis using night marine air temperatures and SST observations from COADS. Because this method is independent from methods proposed by the UK Met Office, the differences indicate uncertainties while similarities indicate where users may have more confidence in the bias correction. The new method gives results which are broadly consistent with the latest UK Met Office bias estimates. However, our bias estimate has a stronger annual cycle of bias in the Northern Hemisphere compared to the Met Office estimate. Both estimates have mid-latitude annual cycles, with the greatest bias in the cold season, and both have a small annual cycle in the tropics. From the 1850s into the early 20th century both bias estimates increase with time, although our estimates increases slightly less than the Met Office estimate over that period. Near-global average temperatures are not greatly affected by the choice of bias correction. However, the need for a bias correction in some periods may introduce greater uncertainty in the global averages. Differences in the bias corrections suggest that this bias-induced uncertainty in the near-global average may be 0.1 C in the 19th century, with less uncertainty in the early 20th century.