One of the major difficulties faced by popcorn breeders is the negative correlation between popping expansion (PE) and grain yield (GY). It is necessary to overcome this difficulty to obtain promising genotypes. One helpful tool in this process is a selection index because it allows multiple features of interest to be selected. Thus, the present study proposes a new and comprehensive selection index applied in 169 half-sib families in UEM-Co1 and UEM-Co2 composites during two cycles of recurrent selection. An experiment was conducted in a 13 x 13 lattice square in the 2004/2005 and 2006/2007 crop years in Maringá, Paraná State, and PE and GY were evaluated. To calculate Fi statistics, the following relative importance (RI) assignments were used: 0.5 for both PE and GY, and 0.70 and 0.30 for PE and GY, respectively. Families were classified according to Fi values such that Fi = 0 indicated that genotypes met the average of those selected by direct selection, Fi < 0 indicated that genotypes fell below the average of those selected, and Fi > 0 indicated that genotypes exceeded the average of those selected. Thus, desirable values of Fi were positive, indicating that the selected families were higher than those families that would be selected by direct selection for both traits. Therefore, we concluded that the novel Fi statistic was satisfactory for family selection because simultaneous and higher gains for both traits in both composites were obtained.