Group signature allows individual members to make signatures on behalf of the whole group. It can be used to constitute a very useful primitive in many settings, such as E-cash, E-auction and E-election. In this paper, we show that the two group signatures proposed by Zhang et al. in 2003 and Kim et al. in 1996 are untraceable by very simple attacks. In contrast to those attacks presented by Wang et al., the techniques developed in this paper are novel and interesting.