Yeast surface-displayed antibody libraries provide an efficient and quantitative screening resource for given antigens, but suffer from typically modest library sizes owing to low yeast transformation efficiency. Yeast mating is an attractive method for overcoming the limit of yeast transformation to construct a large, combinatorial antibody library, but the optimal conditions have not been reported. Here, we report a large synthetic human Fab (antigen binding fragment) yeast surface-displayed library generated by stepwise optimization of yeast mating conditions. We first constructed HC (heavy chain) and LC (light chain) libraries, where all of the six CDRs (complementarity-determining regions) of the variable domains were diversified mimicking the human germline antibody repertoires by degenerate codons, onto single frameworks of VH3-23 and $V{kappa}1$-16 germline sequences, in two haploid cells of opposite mating types. Yeast mating conditions were optimized in the order of cell density, media pH, and cell growth phase, yielding a mating efficiency of ~58% between the two haploid cells carrying HC and LC libraries. We constructed two combinatorial Fab libraries with CDR-H3 of 9 or 11 residues in length with colony diversities of more than $10^9$ by one round of yeast mating between the two haploid HC and LC libraries, with modest diversity sizes of ${sim}10^7$. The synthetic human Fab yeast-displayed libraries exhibited relative amino acid compositions in each position of the six CDRs that were very similar to those of the designed repertoires, suggesting that they are a promising source for human Fab antibody screening.