The Microwave Sounding Units (MSU) aboard the NOAA series of polar orbiting satellites has been used by three groups to monitor the very small trend in the global tropospheric temperature over the 25-year satellite record. To obtain a homogeneous data set, each group made different calibration corrections of the MSUs in the form of fixed biases, and in some cases temperature-dependent adjustments, to each of the nine satellite instruments using data during the overlap periods. Up until now, however, the adjustments are empirically based. To improve the accuracy as well as our understanding of the error sources, this paper develops an alternate, physical approach for intercalibrating the MSU instruments. The paper develops a calibration model for the MSU instrument that includes the errors in the cold space and warm target measurements, as well as the nonlinear factor. Corrections for these calibration errors are estimated using a least squares minimization where the predictors are the differences between all 12 overlapping satellite measurements at low and high latitudes. After applying the calibration corrections, the zonally averaged differences between satellite instruments are no larger than 0.03 K, independent of latitude. It is also found that the tropospheric temperature trend derived from MSU measurements is nearly the same as the surface trend. Furthermore, it now appears that much of the earlier inconsistency between the satellite and surface measurements arises from errors in the MSU calibration correction procedure, which can artificially suppress the temperature trend.