The present invention is directed to a hair dyeing composition containing a dissociative azo dye of the following general formula (1) A-N═N—B  (1) wherein “A” represents a phenyl or naphthyl group which may be substitued; “B” represents an atomic group containing a dissociative proton, with the proviso “A” and “B” are free of sulfo, carboxyl and quaternary ammonium groups. Additionally, the present invention describes a method of dyeing human or animal hair by using such a dye and the use of this direct azo dye for dyeing human or animal hair. The use of this direct azo dye can impart the hair with an extremely vivid color and has less color fading over time.