Biometric systems which are operationally based on human irides are considered to be an effective way of verifying individual identities. However, features extracted from iris images are sometimes characterized by a low degree of stability for intra-class iris samples. In this work, we develop a robust mechanism for selecting the most consistent bits which are present within binary iris features. In the proposed model, we initially form dynamic clusters of invariant positions from some particular iris feature samples and then mark the centers of these clusters as the most consistent locations. Finally, error information from the corresponding iris masks is incorporated for eliminating any effects of noise from the extracted bits. Our work also introduces a formal criterion, termed as t-consistency, for defining the worst-case consistency of IrisCodes with respect to a tolerance threshold. We have tested our proposed model by extracting up to 300 bits from the CASIAv3 Interval and CASIAv4 Thousand databases, wherein we achieved 0.88-consistency and 0.65-consistency of the IrisCodes respectively. We have also obtained competitive recognition accuracy rates for our model in comparison to their baseline results. Hence our study introduces an efficient technique for extracting the most discriminatory binary features from raw iris images.