Assimilation of salinity into ocean and climate general circulation models is a very important problem. Argo data now provide far more salinity observations than ever before. In addition, a good analysis of salinity over time in ocean reanalyses can give important results for understanding climate change. Here it is shown from the historical ocean database that over large regions of the globe (mainly midlatitudes and lower latitudes) variance of salinity on an isotherm S(T ) is often less than variance measured at a particular depth S(z). It is also shown that the dominant temporal variations in S(T ) occur more slowly than variations in S(z), based on power spectra from the Bermuda time series. From ocean models it is shown that the horizontal spatial covariance of S(T ) often has larger scales than S(z). These observations suggest an assimilation method based on analyzing S(T ). An algorithm for assimilating salinity data on isotherms is then presented, and it is shown how this algorithm produces orthogonal salinity increments to those produced during the assimilation of temperature profiles. It is argued that the larger space and time scales can be used for the S(T ) assimilation, leading to better use of scarce salinity observations. Results of applying the salinity assimilation algorithm to a single analysis time within the ECMWF seasonal forecasting ocean model are also shown. The separate salinity increments coming from temperature and salinity data are identified, and the independence of these increments is demonstrated. Results of an ocean reanalysis with this method will appear in a future paper.