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Selection indexes represent the real efforts of a breeding program to obtain genetic gains for various significant traits simultaneously. As such, this study selected superior F5 lines by combined selection for fruit quality using an index based on predicted genotypic values via residual or restricted maximum likelihood/best linear unbiased prediction (REML/BLUP) methodology weighted by agronomic weights. To do so, 97 F5 papaya lines obtained by the single seed descent method, resulting from the biparental cross between the genotypes JS-12 and Sekati, were evaluated for the main traits related to fruit quality. Results of the analysis of deviance and the genetic parameters indicated that there was genetic variability, indicating possible success in the selection process. Based on the selection index, 29 lines were selected as superior for fruit quality with 'Formosa' pattern. The strategy of the selection index combining BLUPs of multiple traits of interest associated with agronomic weights allows maximizing genetic progress while discarding less-promising genotypes. [ABSTRACT FROM AUTHOR]