Correlated information from different genetic sources is absent in most of annual self-pollinated crops using the recurrent selection strategy, which is a breeding strategy that improves crop traits consistently over years. In common bean (Phaseolus vulgaris L.) breeding programs, progenies coming from multiple biparental populations are evaluated across generations of inbred plants with the assumption that the data are not correlated. In this paper, in addition to the effects of progeny, we evaluate the effects of populations and generations and provide information for the selection process in a self-pollinated recurrent selection breeding program. Nineteen progenies were extracted from 20 breeding populations and evaluated at different sowing times across F 3:4 and F 3:5 generations. The evaluated traits were plant architecture, angular leaf spot resistance, grain appearance, and grain yield. Progenies were selected using three methods: means of progenies regardless of generation and population effects; the multigeneration index (MI), which considered the generation effect; and the selection index with parents, populations, progenies, and generations (SIPPPG). We showed that adding variation among progenies correctly weighted for different generations as well as variation among populations yield for an increase in genetic gain. Therefore, selection accuracies of the SIPPPG were the highest for all traits compared with those of MI and when generation and population effects were not considered.