The Microwave Sounding Units (MSU) aboard the NOAA series of polar orbiting satellites has been used to monitor the very small trend in the global tropospheric temperature over the 25 year satellite record. To obtain a homogeneous data set, calibration corrections were made to each of the nine MSU's in the form of fixed biases, and in some cases temperature-dependent adjustments, using data during the overlap periods. Up until now, however, the adjustments are empirically based. To improve the accuracy, this paper develops a calibration model that includes 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 twelve overlapping satellite measurements. After applying the calibration corrections, the globally averaged differences between satellite instruments are no larger than 0.03 K. It is also found that the globally averaged tropospheric temperature trend obtained from MSU channel 2 measurements is 0.17 K/decade, which is nearly the same as the surface trend.