A new inversion method for temperature retrievals from satellite soundings isdescribed. The basis of the inversion method is the radiative transfer equation.Surface observations of temperature, humidity and pressure are alsoincluded. Basis splines have been used to represent the temperature and humidityprofiles. Some physical constraints are also included. This leads toalinear least-squares problem with linear inequality constraints. The extensiontoa nonlinear least-squares problem is discussed.