A new dominant autosomal mutation of Lebistes reticulatus is described, causing a veil-like elongation of fins and increased dichotomous branching of fin rays. The dominant gene Kal, responsible for the formation of veil-fins, can be suppressed by a non-allelic dominant factor Sup. Kal and Sup belong to two different linkage groups. 2. Either Kal or Sup are linked with the dominant allele of the recessive xanthoric factor "blond", because blond veil-fin guppies could not be obtained by recombination. 3. Homozygosity for the recessive wildtype alleles of the gene for veil-fins and of its suppressor, (i.e. + (Kal) /+ (Kal) , + (Sup) /+ (Sup) ) seems to result in postnatal lethality of the males.