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Inverse synthetic aperture radar (ISAR) imaging has long been used as an effective tool to pinpoint target scattering features for signature diagnostic and target identification purposes. Normally, constructing an ISAR image requires data collection in both the frequency and the angular dimensions. If the data are evenly sampled and the sampling rate is dense enough, and provided that the total angular look on the target is small, an ISAR can be obtained by using a two dimensional FFT algorithm. In this paper, we address the case when the angular data are unevenly undersampled. Such a scenario may arise in real-world ISAR data collection when the target is fast manoeuvring or when the angular look on the target by the radar is not dense enough to satisfy the Nyquist sampling rate. We propose an algorithm to overcome the aliasing effect in the cross range dimension and construct ISAR images from seriously undersampled data. To verify the algorithm we reconstruct the radar image of a model VFY 218 aircraft.