The imaginary quadrati elds are dened by the set {a b√−n : a, b ∈ Q} and are denoted by Q(√−n), where n is a square-free positive integer. In this paper we have proved that if α =a √−nc ∈ Q∗(−n)= {a √−nc: a, a2 nc, c ∈ Z, c 6= 0}, then n does not hange its value in the orbit αG, where G =< u, v : u3 = v3 = 1 >. Also we show that the number of orbits of Q∗(√−n) under the a tion of G are 2[d(n) 2d(n 1)−6] and 2[d(n) 2d(n 1) − 4] a ording to n is odd or even, exept for n = 3 for whih there are exa tly eight orbits.Also, the a tion of G on Q∗(√−n) is always intransitive.