We take this opportunity to reread Geertsema's (1972) purely sequential nonparametric procedure for selecting the largest center of symmetry among k(≥2) unspecified populations. Under some mild regularity conditions, Geertsema (1972) obtained first-order asymptotics. In our attempt to revisit this interesting area, we develop an accelerated sequential version of Geertsema's (1972) selection procedure to curtail sampling operations significantly and yet maintain similar first-order asymptotic characteristics. Extensive sets of comments have been provided for various types of immediate comparisons. Overall, the accelerated sequential selection methodology performs remarkably well in comparison with the Geertsema procedure.