In this paper, an investigation is made on how sidelobes can be suppressed in ultrawideband-ultrawidebeam (UWB) Synthetic Aperture Radar (SAR) using apodization. Due to the special properties of UWB SAR such as very wide integration angle and very large relative bandwidth, the support for the spectrum of a SAR image differs distinctively from a rectangle, which is the normal approximation in narrowband-narrowbeam (NB) SAR. The proposal in the paper is to apply non-separable windows to the spectrum, in order to suppress sidelobes. Non-separable windows are shown to give less broadening of mainlobe while maintaining the same suppression of sidelobes in comparison to separable windows. In the comparison, parameters for three different SAR systems are used.