With the widespread adoption of biometric recognition technology, the protection of biometric templates has become crucial for safeguarding user biometric data. However, while protection methods based on random projection can effectively preserve matching performance, they are vulnerable to the reconstruction of original biometric features when multiple projected templates are compromised. To address this issue, a cancellable template protection method, termed Householder-AVET, which is based on Householder matrices and the Absolute Value Equation Transform. It leverages the precise similarity-preserving property of Householder matrices to overcome the matching performance deficiencies inherent in AVET methods that rely on Gaussian random projection. This design allows the key advantage of AVET-its irreversibility-to be fully exploited. Experimental results demonstrate that the proposed Householder-AVET achieves matching performance superior to the conventional AVET on both face and fingerprint databases. Furthermore, it completely surpasses methods that employ random projection on the challenging FVC2004 fingerprint database, highlighting the algorithm's excellent matching performance and robustness.