Ensuring privacy often results in sacrificing the accuracy of iris recognition systems. A primary challenge in contemporary iris biometric privacy methods lies in striking a balance between recognition accuracy and privacy of protected iris templates. Hence, any proposition for privacy-protected iris recognition must prioritize irreversibility, revocability, and unlinkability to uphold robust privacy standards while achieving higher recognition accuracy. This research proposes an approach that stands as a robust solution with acceptable advancement in three challenges: recognition accuracy, privacy protection and computational efficiency. We experimented with an innovative technique that manipulates the columns of an iris template by fusing the bit pattern of the template using the XOR operation. The transformation process is non-linear. This fusion introduces randomness and variability to the fused templates. It also poses enhanced privacy protection. Two datasets were used to validate the proposed approach. Based on the results of dataset 1, the proposed approach accepts genuine users at a rate of 99.11% while it accepts 0.01% of imposters. For dataset 2, the Genuine Acceptance Rate (GAR) is depicted as 81.12% while FAR is at 0.01%. The proposed approach can be applied in practice due to its higher computational efficiency. As further improvements, the research can be extended to more widespread databases and higher-quality iris samples.