Congenital Heart Disease (CHD) is a major public health issue. About 20% of CHD correspond to a misalignment between cardiac segments. We focused on a rare CHD, the congenitally corrected transposition of the great arteries (CCTGA). The aim of this study was to understand the mechanisms and genes that control the alignment of cardiac chambers, and thus lead to the CCTGA. We analyzed a cohort of 44 CCTGA cases (42 sporadic cases and 2 familial cases) of non-syndromic CCTGA by next generation sequencing analysis (whole-genome and whole-exome sequencing). Under the hypothesis of Mendelian model with de novo genomic alterations, no major gene involved in the disease could be identified. Under the hypothesis of a complex model of inheritance with incomplete penetrance, a total gene set of 156 genes matched each of our selection criteria. The highly heterogeneous combinations of susceptibility rare variants, mostly inherited from the healthy mother and father respectively, functionally converge to give rise to the CCTGA phenotype. To prove that a given allele combination is associated with the CCTGA phenotype, we showed a significant enrichment of rare variants in cases, any given deleterious variant combination within the CCTGA gene set being specific to the affected individual. Taken together, the cases could be explained by a mutation load of segregated alleles at loci mostly involved in heart tube looping, outflow tract morphogenesis and establishment of left-right asymmetry. Our data contradict a monogenic mode of inheritance, favouring a multigenic origin of CCTGA, where both parents harbour genetic predisposition variants for the disease (susceptibility alleles) and both transmit this load of variants to the affected offspring, explaining the low recurrence risk.