3GPP-MAC, also called f9, is an integrity scheme adopted by Universal Mobile Telecommunication System as a standard for the 3rd generation wireless communications. In this paper, we investigate the feasibility of improving its efficiency, with the precondition that its security would not be compromised. As we show, the newly proposed f9- enjoys provable security under the solo PRP assumption; more importantly, f9- removes the last block-cipher invocation of f9, which means it needs less time and resources to compute MACs than f9, offering higher efficiency in practice. Furthermore, f9- keeps the main structure of f9 almost unchanged, making it easy to update f9 to f9-in reality.