<p>Cancelable biometrics mitigate privacy and security concerns in biometric-based user authentication by transforming biometric data into non-invertible templates. However, achieving non-invertibility often comes at the cost of reduced discriminability. This paper presents RP-SmXOR, a novel approach for generating cancelable biometric templates, leveraging person-specific real-numbered singular matrices for non-invertible transformation. By combining random permutation, Bitwise-XOR, and the Hadamard product, RP-SmXOR retains and enhances the discriminative information in the templates while addressing the privacy and security concerns associated with traditional biometric authentication. The proposed method was extensively evaluated on seven diverse biometric databases, demonstrating superior performance compared to state-of-the-art random permutation-based techniques. A thorough privacy and security analysis, including brute-force, false acceptance, Attack via Record Multiplicity (ARM), and inverse attacks, along with similarity metrics, confirms the non-invertibility, security, and robustness of the generated templates. Thus, RP-SmXOR adheres to the key principles of cancelable biometrics while significantly improving recognition accuracy and establishing it as a promising solution for secure biometric authentication.</p>