In therapeutic or diagnostic antibody discovery, affinity maturation is frequently required to optimize binding properties. In some cases, achieving very high affinity is challenging using the display-based optimization technologies. Here we present an approach that begins with the creation and clonal, quantitative analysis of soluble Fab libraries with complete diversification in adjacent residue pairs encompassing every complementarity-determining region position. This was followed by alternative recombination approaches and high throughput screening to co-optimize large sets of the found improving mutations. We applied this approach to the affinity maturation of the anti-tumor necrosis factor antibody adalimumab and achieved ~500-fold affinity improvement, resulting in femtomolar binding. To our knowledge, this is the first report of the in vitro engineering of a femtomolar affinity antibody against a protein target without display screening. We compare our findings to a previous report that employed extensive mutagenesis and recombination libraries with yeast display screening. The present approach is widely applicable to the most challenging of affinity maturation efforts.