We introduce a within-sample SNP calling method, called the “butterfly method”, that improves the quality of SNP calling with the Illumina Infinium Omni5-4 SNP Kit. This was done by improving how no-calls are determined from allele signal intensities. High confidence of SNP allele calling is extremely important in forensic genetics and clinical diagnostics. This paper is accompanied by two open-source R packages, omni54manifest and snpbeadchip that make SNP calling easy by helping with bookkeeping and giving easy access to meta-information about the SNPs typed with the Illumina Infinium Omni5-4 Kit (including chromosome, probe type, and SNP bases). We compared the results from our method with those obtained with the Illumina GenomeStudio software (which does not provide sample and SNP specific genotype probabilities or other quality measures), and with whole-genome sequencing (WGS). Given the signal intensities, the SNP calling quality was optimised using a threshold for the a posteriori probability of a SNP belonging to a SNP cluster. By lowering the a posteriori probability threshold for no-calls, we obtained a higher call rate than GenomeStudio. Using a higher a posteriori probability threshold, we achieved a higher concordance with the WGS data than GenomeStudio. Our method had SNP call and concordance rates with WGS data of approximately 99%.