Haplodiploidy is one of the most widespread mechanisms of sex determination in animals. In many Hymenoptera, including all hitherto investigated social species, diploid individuals, which are heterozygous at the sex locus, develop as females, whereas haploid, hemizygous individuals develop as males (single-locus complementary sex determination, sl-CSD). Inbreeding leads to homozygosity at the sex locus, resulting in the production of diploid males, which are usually sterile and constitute a considerable fitness cost. Nevertheless, regular inbreeding without diploid male production is known from several solitary wasps, suggesting that in these species sex is not determined by sl-CSD but alternative mechanisms. Here, we examine sex determination in an ant with regular inbreeding, Cardiocondyla obscurior. The almost complete absence of diploid males after 10 generations of brother-sister mating in the laboratory documents for the first time the absence of sl-CSD and CSD with two or a few unlinked sex loci in a species of social Hymenoptera. Queens, which mated with a brother, appeared to decrease the number of males in their brood, as expected from the relatedness relationships under inbreeding. In contrast, some colonies began to show signs of an inbreeding depression after several generations of sib-mating, such as shortened queen life span, higher brood mortality, and a shift to more male-biased sex ratios in some colonies, presumably due to lower insemination capability of sperm.