Aptamers are typically selected from libraries of random DNA (or RNA) sequences by SELEX, which involves multiple rounds of alternating steps of partitioning and PCR amplification. Here we report, for the first time, non-SELEX selection of aptamers-a process that involves repetitive steps of partitioning with no amplification between them. A highly efficient affinity method, non-equilibrium capillary electrophoresis of equilibrium mixtures (NECEEM), was used for partitioning. We found that three steps of NECEEM-based partitioning in the non-SELEX approach were sufficient to improve the affinity of a DNA library to a target protein by more than 4 orders of magnitude. The resulting affinity was higher than that of the enriched library obtained in three rounds of NECEEM-based SELEX. Remarkably, NECEEM-based non-SELEX selection took only 1 h in contrast to several days or several weeks required for a typical SELEX procedure by conventional partitioning methods. In addition, NECEEM-based non-SELEX allowed us to accurately measure the abundance of aptamers in the library. Not only does this work introduce an extremely fast and economical method for aptamer selection, but it also suggests that aptamers may be much more abundant than they are thought to be. Finally, this work opens the opportunity for selection of drug candidates from libraries of small molecules, which cannot be PCR-amplified and thus are not approachable by SELEX.