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Software reliability deals with the probability that software will not cause the failure of a system in a specified time interval. Software reliability growth models (SRGMs) are used to predict future behaviour from known characteristics of software, like historical failures. With the increasing demand to deliver quality software, more accurate SRGMs are required to estimate the software release time and cost of the testing effort. Software failure predictions at early phases also provide an opportunity for investing in proper quality assurance and upfront resource planning. Up till now, many parametric software reliability growth models (PSRGMs) have been proposed. However, several limitations of them mean that their predictive capacities differ from one dataset to others. In this paper, to enhance the prediction accuracy of existing PSRGMs, a high precision error iterative analysis method (HPEIAM) has been proposed based on the residual errors. In HPEIAM, residual errors from the estimated results of SRGMs are considered as another source of data that can combine the residual error modification with artificial neural network sign estimator. The repeated computation of residual errors by SRGMs improves and corrects the prediction accuracy up to the expected level. The performance of HPEIAM is tested with several PSRGMs using two sets of real software failure data based on three performance criteria. Moreover, we have compared the estimated failures predicted by HPEIAM with genetic algorithm (GA)-based prediction improvement. The results demonstrate that HPEIAM gives an improvement in goodness-of-fit and predictive performance for every PSRGM in initial few iterations.