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In a designated-verifier proxy signature scheme, a user delegates her/his signing capability to another user in such a way that the latter can sign messages on behalf of the former, but the validity of generated signatures can only be checked by the designated verifier. In this paper, we first point out that one such scheme proposed recently by Dai et al. is insecure. To overcome the weaknesses in their scheme, based on the two-party Schnorr signature by Nicolosi et al., we present a new designated-verifier proxy signature scheme which is efficient and secure. Finally, we suggest the use of our scheme in electronic commerce applications, such as sale of digital products (digital music, movies, and books etc.).