One of the major difficulties in simulation of realistic satellite radiances for Observation Systems Experiments and other purposes is modeling the correlated inter-channel noise. In this paper we present a method that quickly and accurately simulates this correlated noise. Given a noise covariance matrix, the algorithm produces multi-channel noise which statistically matches the original matrix. Examples of this technique will be given for the High Resolution Infrared Sounder carried on the NOAA satellites, which can exhibit surprisingly high levels of correlated noise.