At PKC 2008, Plantard et al. published a theoretical framework for a lattice-based signature scheme. Recently, after ten years, a new signature scheme dubbed as the Diagonal Reduction Signature (DRS) scheme was presented in the NIST PQC Standardization as a concrete instantiation of the initial work. Unfortunately, the initial submission was challenged by Yu and Ducas using the structure that is present on the secret key noise. In this paper, we are proposing a new method to generate random noise in the DRS scheme to elimite the aforementioned attack, and all subsequent potential variants.