The traceability is one of the core requirements for group signature schemes. Recently, group signature schemes based on the bilinear mapping were proposed. The bilinearity of a bilinear mapping allows an efficient signature scheme verification for signature schemes based on the Discrete Logarithm type problem. But the bilinearity of a bilinear mapping can be an attack point with respect to the traceability for group signature schemes when it is designed in such a way that the linearity can be preserved. We show that Cheng-Zhu-Qiu-Wang?s group signature schemes [8] based on bilinear mapping have no traceability property due to their improper use of a bilinear mapping in their signature generation and verification step. We also propose security enhanced group signature schemes for both of mini group signature scheme and improved group signature scheme of Cheng-Zhu-Qiu-Wang?s.