Aptamers are typically selected from libraries of random DNA (or RNA) sequences through systematic evolution of ligands by exponential enrichment (SELEX), which involves several rounds of alternating steps of partitioning of candidate oligonucleotides and their PCR amplification. Here we describe a protocol for non-SELEX selection of aptamers--a process that involves repetitive steps of partitioning with no amplification between them. Non-equilibrium capillary electrophoresis of equilibrium mixtures (NECEEM), which is a highly efficient affinity method, is used for partitioning. NECEEM also facilitates monitoring of bulk affinity of enriched libraries at every step of partitioning and screening of individual clones for their affinity to the target. NECEEM allows all clones to be screened prior to sequencing, so that only clones with suitable binding parameters are sequenced. The entire protocol can be completed in 1 wk, whereas conventional SELEX protocols take several weeks even in a specialized industrial facility.