Motivation: Next-generation sequencing tools have enabled producing of huge amount of genomic information at low cost. Unfortunately, presence of sequencing errors in such data affects quality of downstream analyzes. Accuracy of them can be improved by performing error correction. Because of huge amount of such data correction algorithms have to: be fast, memory-frugal, and provide high accuracy of error detection and elimination for variously-sized organisms. Results: We introduce a new algorithm for genomic data correction, capable of processing eucaryotic 300 Mbp-genome-size, high error-rated data using less than 4 GB of RAM in less than 40 minutes on 16-core CPU. The algorithm allows to correct sequencing data at better or comparable level than competitors. This was achieved by using very robust KMC~2 $k$-mer counter, new method of erroneous regions correction based on both $k$-mer counts and FASTQ quality indicators as well as careful optimization. Availability: Program is freely available at http://sun.aei.posl.pl/REFRESH/reckoner. Contact: sebastian.deorowicz@polsl.pl