Imperfectly expanded supersonic jets under strong screech could generate both fundamental screech tones and multiple tones at the harmonics of the fundamental frequency. The paper compares the fundamental frequency of jets from both AR = 3 (Aspect Ratio) and AR = 4 rectangular nozzles, and conducts analysis of harmonics on Sound Pressure Level (SPL) spectrums of jet noise. The research suggests that the fundamental frequency of the first two- or three-order harmonics increases when the Nozzle Pressure Ratio (NPR) decreases, whereas the highest order harmonic decreases when the NPR decreases. Besides, the paper also observes the differences between the highest order harmonics and other harmonics that have never been reported before. Further analysis on flow field schlieren of AR = 3 nozzle indicates that the highest order harmonic is the outcome of interaction between second shock-cell and nonlinear instable wave. The revolution of these high order harmonics can provide guidance for the prevention of small-scale structure fatigue damage. Moreover, the distribution test of the noises is also carried out to verify the high order harmonics anomaly, and indicate that the jet noise spreads mainly towards downstream while screech towards upstream. In addition, the broadband shock-associated noise spreads vertical to the jet flow and exhibits the feature of directivity.