This paper addresses the issue of finding an optimal estimator of the normal population mean when the coefficient of variation is unknown. The paper proposes an “Efficient Iterative Estimation Algorithm Using Sample Counterpart of the Searles’ Normal Mean Estimator”. The estimators per this strategy have no close form, and hence are not amenable to any analytical study determining their relative efficiencies as compared to the usual unbiased sample mean estimator. Nevertheless, we examine these relative efficiencies of our proposed iterative estimators with respect to the usual unbiased estimator by means of an illustrative numerical empirical study. The MATLAB 7.7.0.471