A β″ superlattice structure, with the ideal stoichiometrical formula AgAuZn2 and isoinorphous with that of Heusler alloys, has been found existing over a quite wide range of composition. It is, in fact, a superstructure of the β′ ordered structure. Its formation is accompanied by a sudden lattice contraction. The effect of gradual substitution of Ag by An on the atomic distribution has been stndied systematically. It is shown that the Au atoms introduced simply replace the Ag atoms more or less in a random manner, the positions of Zn atoms not being affected. Tho decrease of the degree of order as deviating from the stoichiometrical formula is not merely due to the deviation from the ideal chemical composition; some disordering among the Ag and Au atoms also occurs. High temperature investigation of Ag-rieh alloys shows that the temperature of β′-β transformation increases with Au content and that the β-phase structure exists only at high temperatures. The presence of even a minute amount of Au stablizes the β′ structure obtained by quenching very remarkably. On the other hand, the β′ structure of Au-rich alloys persists from room temperature probably to the melting point.