In addition to the conventional fixed-source method, the iterative k-source (IKS) method is another Monte Carlo algorithm used for solving fixed-source problems. In contrast to the fixed-source method, the IKS method iterates the fission sources for each generation, which is similar to the k-eigenvalue calculation. The IKS method does not require following long-chain fission reactions until the end, even for a nearly critical subcritical system. The source-multiplication factor, ks, which is supposed to be less than unity, is calculated for each cycle. However, ks occasionally or frequently exceeds unity in a nearly critical system owing to statistical fluctuations, in which case the result of the IKS method is biased. To eliminate this bias, the frequency at which ks exceeds unity should be minimized by increasing the source size per cycle. As demonstrated in this study, the computational efficiency of the IKS method is three to ten times that of the conventional fixed-source method.