The visible/infrared imaging radiometer suite (VIIRS) is now onboard the first satellite platform managed by the Joint Polar Satellite System of the National Oceanic and Atmospheric Administration and NASA. It collects scientific data from an altitude of approximately 830 km in 22 narrow bands located in the 0.4-12.5 μm range. The seven visible and near-infrared (VisNIR) bands in the wavelength interval between 0.4-0.9 μm are known to suffer from the out-of-band (OOB) responses--a small amount of radiances far away from the center of a given band that can pass through the filter and reach detectors in the focal plane. A proper treatment of the OOB effects is necessary in order to obtain calibrated at-sensor radiance data [referred to as the Sensor Data Records (SDRs)] from measurements with these bands and subsequently to derive higher-level data products [referred to as the Environmental Data Records (EDRs)]. We have recently developed a new technique, called multispectral decomposition transform (MDT), which can be used to correct/remove the OOB effects of VIIRS VisNIR bands and to recover the true narrow band radiances from the measured radiances containing OOB effects. An MDT matrix is derived from the laboratory-measured filter transmittance functions. The recovery of the narrow band signals is performed through a matrix multiplication--the production between the MDT matrix and a multispectral vector. Hyperspectral imaging data measured from high altitude aircraft and satellite platforms, the complete VIIRS filter functions, and the truncated VIIRS filter functions to narrower spectral intervals, are used to simulate the VIIRS data with and without OOB effects. Our experimental results using the proposed MDT method have demonstrated that the average errors after decomposition are reduced by more than one order of magnitude.