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In noise radars, measuring the cross-correlation between transmitted and received signals is a common method of signal processing. However, it brings a lot of unwelcome sidelobes that can mask weak echoes of far targets. There are many classical and modern methods of masking effect removal which are based on signal processing in the receiver side. In this study, a method of waveform design is presented and its ability to reduce masking effect is compared with that of radars using purely random waveforms. The method starts with choosing an arbitrary subsequence and continues with attaching new subsequences to the previous ones in a way that the sidelobe levels reduce. In addition, the performance of applying the well-known CLEAN algorithm to a purely random waveform and the presented waveform are considered in detail. Moreover, the waveform randomness is measured and compared with purely random waveforms. By means of computer simulations, it is illustrated that the proposed waveforms can produce smaller correlation sidelobes, while preserving their randomness characteristics.