A Continuous Double Auction (CDA) allows many buyers and sellers to continuously submit bids for the purchase and sale of a commodity (e.g., online share trading). Protocols protecting privacy in this type of powerful market mechanism are essential. However, until recently the security of CDAs has been given limited coverage. This paper describes a new scheme for conducting an anonymous and secure CDA. We show that any existing secure group signature scheme can be used to implement a CDA which has the following characteristics: unforgeability, anonymity, unlinkability, exculpability, coalitionresistance, verifiability, robustness and traceability. Furthermore, bidders can be added to and removed from the auction without affecting the process of the auction. Our scheme is more flexible than the only existing secure CDA scheme, which in contrast provides only a limited subset of these characteristics.