Abstract-A convertible multi-authenticated encryption (CMAE) scheme allows a group of signers to cooperatively produce a valid authenticated encryption signature and still preserves the characteristic of convertible authenticated encryption (CAE) schemes. In 2008, Tsai proposed a CMAE scheme based on the intractability of one-way hash functions and discrete logarithms. However, we find that Tsai's scheme cannot provide the semantic security of the message and the computational efficiency of this scheme is rather high. In this paper, we propose a secure CMAE scheme, in which it enhances the semantic security of the message to overcome the defect in Tsai's scheme. Moreover, by compared with Tsai's scheme, the performance of the proposed scheme is more efficient than Tsai's in term of computational complexity.