Neutron spectrum unfolding is a crucial process in radiation protection and dosimetry. Unfolding codes using iterative algorithms require a criterion to stop the iterations. One approach often relies on the Root Mean Square Error (RMSE) criterion to assess the convergence of iterative algorithms. The aim of this work is to present a new criteria: Average Ratio Scaled (AVGS) and Relative Change in AVGS (dAVGS) to address specific challenges associated with RMSE. Extensive validation tests were conducted, covering a range of scenarios with results showing high level of agreement between the unfolded spectra and the reference.