Group signatures, introduced by Chaum and van Heyst at Eurocrypt'91, allow individual members of a group to sign messages on behalf of the group while remaining anonymous. Furthermore, in case of disputes later a trusted authority, who is given some auxiliary information, can identify the signer. In this paper, we introduce a new kind of group signature scheme, called “convertible group signatures”. In these schemes, in addition to the properties of group signatures, release of a single bit string by the signer turns all of his group signatures into ordinary digital signatures. Then, we present a non-interactive selectively convertible group signature scheme.